# when solving for all solutions how do I work out this problem: cos4(alpha)=cos2(alpha) and when verifying each identity how do I complete this problem: sin (alpha/2)=sec alpha -1/2sin (alpha/2)sec alpha

114,514 results

1. ### precal

when solving for all solutions how do I work out this problem: cos4(alpha)=cos2(alpha) and when verifying each identity how do I complete this problem: sin (alpha/2)=sec alpha -1/2sin (alpha/2)sec alpha
2. ### trig

FInd the exact value pf the 6 trig function of alpha Given: point (-2,-6) on the terminal side of the angle in standard position sin alpha cos alpha tan alpha sec alpha csc alpha cot alpha
3. ### Trigonometry

Find the counterexample to shows that the equation sec (alpha) - cos (alpha) = sin (alpha) sec (alpha) is not an identity. Please explain.
4. ### algebra

if sin alpha is 0.28° where 0° is less than or equal to alpha less than or equal to 90°, evaluate cos alpha, tan alpha, sec alpha, cosec alpha and cot alpha. please help, it's urgent.
5. ### trig

Please find sin (alpha/2) and cos (alpha/2) sec alpha = 3, -pi/2 < alpha < 0
6. ### trig

express 20sin theta + 4 cos theta as R sin(theta + alpha) R sin(theta + alpha) = R cos(alpha)sin(theta) + R sin(alpha)cos(theta) ----> Rcos(alpha) = 20 Rsin(alpha) = 4 The x-y coordinates of a point on a circle of radius R that makes an angle og alpha with the positive x-...
7. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x + 6 are divided by ( x + 1 ) and ( x - 2 ) ...
8. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x + 6 are divided by ( x + 1 ) and ( x - 2 ) ...
9. ### Math

If alpha and beta are the zeros of the polynomial ax^2 + bx + c then evaluateA. (alpha)^2 / beta + (beta)^2 / alpha B. alpha^2 .beta + alpha.beta^2 C. 1/(alpha)^4 + 1/(beta)^4. Please work the complete solution.
10. ### trig

evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(beta-alpha) C. cos(alpha-beta)
11. ### mathematics

If cos 9 alpha = sin alpha 9 alpha < 90 degree then 5 alpha =
12. ### mathematics

If cos 9 alpha = sin alpha 9 alpha < 90 degree then 5 alpha =
13. ### trigonometry

given that sin alpha/2 = 2/3, and that alpha/2 is in quadrant II, determine the exact values of all trig functions for alpha.
14. ### trig

Find sin (alpha/2) and cos (alpha/2) sin alpha = 3, -pi/2 < alpha <less then or equal to 0 How to get the answer of sin (alpha/2) = -1/square root 3, cos(alpha/2) = square root 6/3?
15. ### Trigonometry

Prove that tan^2(alpha)-1+cos^2(alpha)sin^2(alpha) Please Explain
16. ### MATH

knowledge : point (-3,-4)is on the terminal arm of an angel (alpha) in stander position.verify that (sin alpha)2 + (cos alpha )2 =1
17. ### Trig

assume A= alpha using complementary rule how do I solve for alpha? cos(2A+40) =sin(3A-60) I don't understand how to start the question. What are the steps in solving for alpha. Do i get cos to equal sin somehow?
18. ### Trigonometry

Write cos(-83degrees) as a function of a positive angle Prove that tan^2(alpha)-1+cos^2(alpha)=tan^2(alpha)sin^2(alpha)
19. ### maths

if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of (i)alpha^2+beta^2 (ii)1/alpha^2+1/beta^2 (iii)(r)alpha/beta+(r)beta/alpha (iv)alpha^-1+beta^-1
20. ### maths (trigonometry)

sin(alpha-bita)=1/2 and cos(alpha+bita)=1/2, where alpha and bita are positive acute angles then what is the value of alpha and bita
21. ### Trigonometry

Given that sin alpha = 15/17 and -360 <alpha<360 find all values of alpha to two decimal places. Help Please!
22. ### physics

Two radar stations A and B, are separated by horizontal distance of (a=500 metres), they both track the position of a plane C by recording angles (alpha), and (beta) at 1 second intervals. time (sec) 9 10 11 the angle A(alpha) 54.80 54.06 53.34 the angle B (beta) 65.59 64.59 ...
23. ### Math Proof

Prove: let alpha be a lower bound of a subset E of an ordered set S. If alpha exist in E, then alpha= infE(greatest lower bound of E). PF: Already have alpha is a lower bound of E. Let lambda be a different lower bound of E. If alpha precedes lambda, the lambda will not be a ...
24. ### another college math question

Please teach me. I am completely blank with it. :( Let alpha = (3+sqrt(-3))/2 belongs to Q[sqrt(3)]. Show that if x is congruent to 1 mod alpha, then x^3 is congruent to 1 (mod alpha)^3. Similarly, show that if x is congruent to -1 mod alpha, then x^3 is congruent to -1 (mod ...
25. ### Trigonometry

Find the exactly value of sin2(alpha) if cos(alpha) = 4/5 (alpha in Quadrant I)
26. ### Trigonometry

Three oil platforms, Alpha, Beta and Gamma are situated in the North Sea.Beta is 12 km from Alpha and is on a bearing of 145 degrees from Alpha.Gamma is 16 km from Alpha and is on a bearing of 220 degrees from Alpha.Find the distance of Beta from Gamma. (Not sure how to ...
27. ### physics

The acceleration of a bus is given by $$a_{x}(t)= \alpha t$$, where $$\texttip{\alpha}{alpha}$$ = 1.10$${\rm m/s^3}$$ is a constant.
28. ### Math

using sin(alpha-beta)=(sin alpha)(cos beta)-(cos alpha)(sin beta) use the identity to derive the result proof for : sin(alpha-beta) PLEASE PLEASE PLEASE HELP
29. ### Math

how i solve this two equations ib order to find alpha and beta 2=cos(alpha)+1.341cos(beta) 2=sin(alpha)-1.341sin(beta)
30. ### maths --.

If sin theeta=3/5 , cos alpha= -12/13 and theeta,alpha both lie in 2nd quadrant,find the value of tan (theeta+alpha).
31. ### calculus

Interference Two identical tuning forks are struck, one a fraction of a second after the other. The sounds produced are modeled by f1(t) = C sin(wt) and f2(t) = C sin(wt + Alpha). The two sound waves interfere to produce a single sound modeled by the sum of these functions f(t...
32. ### Math

sec(alpha) = -4(√(5))/5 find exact values at alpha for the remaining five trig functions
33. ### Math

The terminal side of an angle alpha (in standard position) contains the point (-3,-4). Find sec alpha.
34. ### Nuclear Physics

Consider an alpha particle with kinetic energy E_ (alpha) which is incident on a material. Show that the distance traveled, ∆x, by the alpha particle after it has lost an amount of energy ∆E, in the material, can be found by the following equation: ∆x=Range (...
35. ### Nuclear Physics

Consider an alpha particle with kinetic energy E_ (alpha) which is incident on a material. Show that the distance traveled, ∆x, by the alpha particle after it has lost an amount of energy ∆E, in the material, can be found by the following equation: ∆x=Range (...
36. ### trig

in the diagram below.A,B and C are three points in the same horizontal plane and AD is a vertical tower.AC=AB=x and DC=DB.the angle of elevetion of D from C is alpha and DB^C=theta 1.express DC in terms of x trigonometry value of alpha 2.prove that BC=2xcostheta/cos alpha
37. ### Calculus

The question will first read in English followed by a reading in French. *************************************** If alpha + 2 beta = pi/4 AND tan beta = 1/3. What would tan alpha mesure? (Keep in mind that pi/4 is the same as 45 degrees.) Si alpha + 2 beta = pi/4 ET tan beta...
38. ### business law

Alpha Corporation in Boston offers a job to Carol, who lives in Des Moines, Iowa. Carol orally agrees with Alpha to work in Boston for two years. She moves her family to Massachusetts and begins to work. Three months later, she is fired for no stated cause. She files a suit ...
39. ### Math

Given that sin alpha=4/sqrt65, pi/2<alpha<pi, and cos beta=-3/sqrt13, tan beta>0, find the exact value of tan(alpha+beta)
40. ### Statistics

We conducted a hypothesis test for a population parameter at alpha = 0.05 and we failed to rejected Ho. If we decided to use alpha = 0.10, how would our conclusion change? A) At alpha = 0.10, we would still fail to reject HO. B) At alpha = 0.10, we would reject HO. C) It is ...
41. ### maths

Given that the roots of 2x^2-4x+5 are alpha and beta,find the value of ... (i)alpha^3beta^3 (ii)(alpha-beta)^2
42. ### maths

prove that the length of the perpendicular from the origin to the straight line joining the two points having coordinates ( a cos alpha, a sin alpha) and (a cos beta, a sin beta) is a cos { ( alpha + beta)/2}.
43. ### physics

A golfer takes two putts to sink the ball, one is (81.6 ft, 31.7 degrees N of E) and the other is (3.20 ft, 53.4 degrees W of N). What is the displacement of the single putt that would sink the ball on the first try? Well, what I did was make a diagram of the two vectors, I ...
44. ### CHEM

the nuclide 232 Th 90 is radioactive. when one of the atoms decays, a series of alpha and beta particle emission occurs, taking the atom through many transformations to end up as an atom of 208 Pb 82. How many alpha particles are emitted in converting 232 Th 90 into 208 Pb 82...
45. ### Physics

Q)1 : Alpha particles travel through a magnetic field of 0.360T and are deflected in an arc of 0.0820m. Assuming the alpha particle are perpendicular to the field, what is the energy of an individual alpha particle?
46. ### Statistics

We conducted a hypothesis test for a population parameter at alpha = 0.01 and we failed to rejected Ho. If we decided to use alpha = 0.05, how would our conclusion change? A) At alpha = 0.05, we would still fail to reject HO. B) At alpha = 0.05, we would reject HO. C) It is ...
47. ### Physics

The nucleus of 8Be, which consists of 4 protons and 4 neutrons, is very unstable and spontaneously breaks into two alpha particles (helium nuclei, each consisting of 2 protons and 2 neutrons). (a) What is the force between the two alpha particles when they are 5.00x10^-15 m ...
48. ### Chemistry

Why is an alpha particle written as a helium (He) nucleus? A. An alpha particle has two protons and two neutrons; it is essentially the nucleus of a helium atom. B. Helium is a common element that is often present in small forms; the alpha particle was misidentified in early ...
49. ### physics

Rutherford fired a beam of alpha particles (helium nuclei) at a thin sheet of gold. An alpha particle was observed to be deflected by 90.0°; its speed was unchanged. The alpha particles used in the experiment had an initial speed of 2.2 ✕ 10^7 m/s and a mass of 6.7 ✕ 10...
50. ### MATHEMATICS

alpha +beta=pie/2 & beta+gama=alpha then tan alpha=?
51. ### Math

alpha and beta the root of x^2+mx+m^2-8=0 find alpha^2+(alpha*beta)+bata^2
52. ### Nuclear Chem

the nuclide 232 Th 90 is radioactive. when one of the atoms decays, a series of alpha and beta particle emission occurs, taking the atom through many transformations to end up as an atom of 208 Pb 82. How many alpha particles are emitted in converting 232 Th 90 into 208 Pb 82...
53. ### trig

The terminal side of angle alpha is in the fourth quadrant, and sin alpha=-1/2, find the values of the other functions.
54. ### math

alpha+beta=22/7/2 and sin alpha=1/3 then what is sinbeta
55. ### ChEmIsTrY

Alpha rays are really a. electrons b. helium nuclei c. electromagnetic waves I think the answer is B because the alpha particle is a helium nucleus. But I'm confused because if the alpha PARTICLE is a helium nucleus, would alpha RAYS be helium nuclei? Please explain.
56. ### Calculus Help

I have looked high and low to figure out how to start this question. I have no clue! Any help would be great!! Rainbows are formed when light strikes raindrops and is reflected and refracted. The Law of Refraction states that (sin alpha)/(sin beta) = k, where k equals 1.33 (...
57. ### statistics

Suppose that a researcher normally uses an alpha level of .01 for hypothesis test, but this time uses an alpha level of .05. What does this change in the alpha level do to the amount of power? What does it do to the risk of a Type I error?
58. ### math

If cotalpha = root 3, calculate (sin alpha)*(cot alpha) - cos^2alpha exactly. can you plzzz help urgent because I have a major test tommorow thnx for all your help
59. ### stats

In a given situation, suppose H0 (null hypothesis) was not rejected at alpha= .02. Would H0 also be retained at alpha = .01? would H0 also be retained at alpha = .05? I'm thinking yes and can't tell. I agree If you did not reject Ho at P = .02, You would definitely not reject ...
60. ### Physics

Suppose that you are at the top of a (rigid) rocket which is half a light year tall. If the rocket is accelerating such that your proper acceleration is 1g, What is the proper acceleration at the bottom of the rocket? B = F c2 c2 􀀀  F : This is one of the equations ...
61. ### Chemistry

(a) The phase diagram of the binary system, neodymium-scandium ( Nd-Sc ) is given below. There are two polymorphs in the solid state: alpha which is hexagonal close packed (HCP) and beta which is body-centered cubic (BCC). Identify all phases present at points 1, 2, and 3. ...
62. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution.
63. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution.
64. ### Math

Let Alpha and Beta be the zeros of the cubic polynomial x^3 + ax^2 + bx + c satisfying the relation Alpha * Beta -1 = 0. Prove that : c^2 + ac + b + 1 = 0. Please work the complete solution
65. ### maths

If alpha and beta are the zeros of the polynomial p(x)=x^2+x+1 then find the value of 1÷alpha+1÷beta 2)alpha^2+beta^2
66. ### trig

If sin alpha = -3/5, sin beta = -5/13, P(alpha) is in the third quadrant, and P(beta) is in the fourth quadrant, find the following: a) sin (alpha - beta)
67. ### astro

ProximaCentauriisapproximatelythesamedistancefromEarth(slightly less than 4.3 light years) as Alpha Centauri A, but it has an apparent magnitude of +11.05, compared to Alpha Centauri A’s magnitude of -0.01. How much more luminous is Alpha Centauri A than Proxima Centauri?
68. ### Trig.

I have answers for these problems, but I wanted to check if I had them right because I wasn't sure on some of them....Thanks. Solve the triangle: 1. a=4, b=8, alpha=30 deg. answer- beta=90 deg., gamma=60 deg., c=7 2. a=5, b=7, alpha=30 deg. answer- beta=44 deg., gamma=106 deg...
69. ### Physics

When U238 decays into Pb206 via alpha and beta decay, what are the byproducts of the decay? A) 8 alpha particles and 6 beta rays. B) 8 alpha particles, 6 electrons, 6 neutrinos, and energy. MY ANSWER . C) 16 alpha particles, 16 beta rays, and energy. D) 16 deuterons and 6 ...
70. ### Physical Science

When U238 decays into Pb206 via alpha and beta decay, what are the byproducts of the decay? A. 8 alpha particles and 6 beta rays. B. 8 alpha particles, 6 electrons, 6 neutrinos, and energy C. 16 alpha particles, 16 beta rays, and energy D. 16 deuterons and 6 electrons. PLEASE ...
71. ### Pre Calc.

Use the sum or difference identity to find the exact value of sin255 degrees. My answer: (-sqrt(2)- sqrt(6)) / (4) Find the value of tan (alpha-beta), if cos alpha= -3/5, sin beta= 5/13, 90<alpha<180, and 90<beta<180. My answer: -33/56 Which expression is ...
72. ### Physics grade 12

A horizontal beam of alpha particles are injected with a speed of 1.3x10^5 m/s into a region with a vertical magnetic field of magnitude 0.155T. A- How long does it take for an alpha particle to move half way through a complete circle? B- If the speed of the alpha particle is ...
73. ### maths

Q1). If the zeroes of he polynomial f(x)=ax^3+3bx^2+3cx+d are in A.P then show that 2b^3 -3abc +a^2d=0 (detailed solution .....) Q2)if alpha, beta, gamma are the roots of equation x^3-3x+11=0 then find the equation whose roots are (alpha + beta),(beta + gamma),(gamma +alpha...
74. ### statistics

A researcher administered a treatment to a sample of participants selected from a population of 80. If the researcher obtains a sample mean of M=88. Which combination of factors is most likely to result in rejecting the null hypothesis? a, alpha level=0.01 and standard ...
75. ### Plz help Physics-bobpursley

Bob, please confirm if I got this right and if not, please help to solve 1)A wire has a resistance of 10 ohm at 20 deg celsius and 13.1 ohm at 100 deg celsius. Obtain a value for its temperature coefficient of resistance. ans I got is this= using Rt = Ro (1 + alpha(T-To)) 13.1...
76. ### Calculus 3

A ball is thrown at an angle of 45 degrees to the ground. If the ball lands 90m away, what is the initial speed of the ball? I know you use x(t)=(v*cos(alpha))t and y(t)=(v*sin(alpha))t-g/2t^2 but I'm still really confused about what to do. Please show all work. Thank you.
77. ### maths

If alpha beta are the roots of a^2 +bx + c = 0. find the values of (beta/alpha^2)+ (alpha/beta^2)
78. ### Physics?

In Rutherford's scattering experiments, alpha particles (charge = +2e) were fired at a gold foil. Consider an alpha particle, very far from the gold foil, with an initial kinetic energy of 2.0 MeV heading directly for a gold atom (charge +79e). The alpha particle will come to ...
79. ### physics

In Rutherford's scattering experiments, alpha particles (charge = +2e) were fired at a gold foil. Consider an alpha particle, very far from the gold foil, with an initial kinetic energy of 3.3 MeV heading directly for a gold atom (charge +79e). The alpha particle will come to ...
80. ### math

This is the problem given: The side of a hill faces due south and is inclined to the horizontal at an angle alpha. A straight railway upon it is inclined at an angle beta to the horizontal. If the bearing of the railway is gamma east of north, show that cos(gamma) = cot(alpha)...
81. ### Physics help!

An alpha particle(charge +2e) is sent at a speed towards a gold nucleus( +79e ). 1) what is the electric force acting on the alpha particle when it is 2.0 x 10^-14 m from the gold nucleus. 2) if the alpha particle came to a stop at this position after traveling 8.22 x 10^-13, ...
82. ### Torque, Physics

A ladder of length 2L and mass M is positioned on level ground leaning against a wall such that the angle between the ladder and the horizontal is α. The coeﬃcient of static friction between the ladder and the wall and between the ladder and the ground is μstatic =0 .65. ...
83. ### Pre-calculus

Given that alpha=(14pi/3) what is the least positive angle coterminal with alpha?
84. ### math

a body is projected at an elevation alpha with a velocity of 9.8m/s in what time Wii be direction of motion be alpha/2?
85. ### stats

H0: pi<=.60 versus H1:pi>=.60, alpha:.05 x:56 n:80 I really don't get where Alpha is involved, pls help. Thanks
86. ### statistics

H0: pi<=.60 versus H1:pi>=.60, alpha:.05 x:56 n:80 I really don't get where Alpha is involved, pls help. Thanks
87. ### Physics

Two cars are drag racing, starting from rest at t = 0, on a straight and level road. Team Alpha's car produces acceleration ax = alpha t^(-1/2) ; while Team Beta's car produces acceleration ax = Beta ; for all t > 0, where alpha and beta are positive constants with suitable...
88. ### Physics

A uniform cylindrical spool of mass M and radius R unwinds an essentially massless rope under the weight of a mass m. If R = 12 cm, M = 400 gm and m = 50 gm, find the speed of m after it has descended 50 cm starting from rest. Solve the problem twice: once using Newton's laws ...
89. ### kvno.1

if alpha ,beta are the zeroes of a polynomial,such that alpha+beta=6 and alpha into beta=4 ,then write the polynomial.
90. ### Physics

Two cars are drag racing, starting from rest at t = 0, on a straight and level road. Team Alpha's car produces acceleration ax = alpha t^(-1/2) ; while Team Beta's car produces acceleration ax = Beta ; for all t > 0, where alpha and beta are positive constants with suitable...
91. ### maths

a ladder rests against a wall at an angle alpha to the horizontal its foot is pulled away from the wall through a distance a so it slides at bita making an angle bita with the horizontal show that a upon b=cos alpha-cos bita upon sin bita-sin alpha?

Two cars are drag racing, starting from rest at t = 0, on a straight and level road. Team Alpha's car produces acceleration ax = alpha t^(-1/2) ; while Team Beta's car produces acceleration ax = Beta ; for all t > 0, where alpha and beta are positive constants with suitable...
93. ### Math

if alpha and beta are the zeroes of the polynomial f(x)=x^2-3x-2 , find a quadratic polynomial whose zeroes are 1/2(alpha)+beta and 1/2(beta)+alpha ? Please... i have no idea !!
94. ### biology AS level

draw a glycogen that contains alpha 1,4 and alpha 1,6 glycosidic bonds. please could someone point me in the right direction.
95. ### Physics

An alpha particle has a kinetic energy of about 5 MeV after they are far from the nucleus. Use this information to estimate the size of a nucleu by assuming that the alpha particle leaves the edge of the nucleus with zero kinetic energy and that the electrostatic potential ...
96. ### physics

An alpha particle (charge = +2.0e) is sent at high speed toward a gold nucleus (charge = +79e). What is the electric force acting on the alpha particle when the alpha particle is 1.7 multiplied by 10-14 m from the gold nucleus? N
97. ### physics

An alpha-particle collides with an oxygen nucleus which is initially at rest. The alpha-particle is scattered at an angle of 67.0 degrees from its initial direction of motion, and the oxygen nucleus recoils at an angle of 52.0 degrees on the other side of this initial ...
98. ### Physics

1. A gold atom has a mass of 3.287 • 10-25 kg and is at rest. It emits an alpha particle that has a mass of 6.646 • 10-27 kg. In this process, the gold atom is transformed into an iridium isotope. The alpha particle has a speed of 3.40 • 106 m/s. A. What is the absolute ...
99. ### Pre-calculus

What is the general expression in degrees for the measure of all angles coterminal with alpha when alpha=173 degrees?
100. ### trignometry

if alpha and beta are 2 different values of θ lying between 0 and 2π which satisfy the equation 6cosθ+8 sinθ=9 find the value of sin alpha + beta.i want the answer by quadratic method. can u help solving sum by that method