
1) Find all the solutions of the equation in the interval (0,2pi). sin 2x = sqrt3/2 I know that the angles are 4pi/3 and 5pi/3 and then since it is sin I add 2npi to them. 2x = 4pi/6 + 2npi 2x = 5pi/3 + 2npi Now I know that I have to divide by 2 but that

1) Find all the solutions of the equation in the interval (0,2pi). sin 2x = sqrt3/2 I know that the angles are 4pi/3 and 5pi/3 and then since it is sin I add 2npi to them. 2x = 4pi/6 + 2npi 2x = 5pi/3 + 2npi Now I know that I have to divide by 2 but that

Find all the soultions of the equation in the interval (0,2pi) sin 2x = sqrt3 /2 sin sqrt3 /2 is 4pi/3 and 5pi/3 in the unit circle 2x= 4pi/3 + 2npi 2x=5pi/3 + 2npi I do not know what to do at this point.

Find all the soultions of the equation in the interval (0,2pi) sin 2x = sqrt3 /2 sin sqrt3 /2 is 4pi/3 and 5pi/3 in the unit circle 2x= 4pi/3 + 2npi 2x=5pi/3 + 2npi I do not know what to do at this point

1. On the interval [0, 2pi] what are the solutions to the equation sin3xcos2x = cos3xsin2x + 1? pi/10 and pi/2? 2. What is the value of tan75degrees? √(3) + 1)/(1  √(3))? 3. Value of cos(130degrees)cos(130degrees) +


Please can you help me with this question? Choose the option which is a false statement: A arctan(tan2/3pi))=1/3pi B arccos(cos(3/4pi))=3/4pi C sin(arcsin(1/2pi))=1/2pi D arcsin(1/2squareroot3)=1/3pi E arcsin(sin(3/4pi))=1/4pi F arccos

1. 3cot^2 (x)  1 = 0 My answer: pi/3, 2pi/3, 4pi/3, 5pi/3 2. 4cos^2 (x)  1 = 0 My answer: pi/3, 2pi/3, 5pi/3, 4pi/3 3. 2sin (x) + csc (x) = 0 My answer: unknown lol i got to the part: sin^2 (x) = 1/2 4. 4sin^3 (x) + 2sin^2 (x)  2sin^2 (x) = 1

Find all solutions in the interval [0,2pi) 4sin(x)cos(x)=1 2(2sinxcosx)=1 2sin2x=1 2x=1/2 x= pi/6, and 5pi/6 Then since its 2x i divided these answers by 2 and got pi/12 and 5pi/12 However, when i checked the answer key there solutions 13pi/12 and 17pi/12

1. Which expression is equivalent to cos 2theta for all values of theta ? cos^2 theta – sin^2 theta ~ cos^2 theta – 1 1 – 2 sin^2 theta 2 sin theta cos theta 2. Use a half–angle identity to find the exact value of sin 105°. 1/2(sqrt)(2 + Sqrt3)

Find all solutions of 4(sin(x)**2)8cos (x) 8 = 0 in the interval (2pi, 4pi). (Leave your answers in exact form and enter them as a commaseparated list.)

determine all co terminal angles that lie in the interval 4pi less thank or equal to theta less than or equal to 4pi, for the following angles. a) 3pi/2 b) 5pi/3

use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(pi/6), cos(5pi/3) and tan (4pi/3). I know that sin (pi/6) = 1/2 and cos (5pi/30 = 1/2 and

Let f(x)=sqrt(x) and g(x)=sin(x). Find f*g and determine where f*g is continuous on the interval (4pi, 4pi)

Find the solution. 1. sqrt2 sin x + 1 = 0 My ans: x = 5pi/4 + 2npi and 7pi/4 + 2npi 2. sec x  2 = 0 My ans: x = pi/3 + 2npi and 5pi/3 + 2npi

Eq of curve is y=b sin^2(pi.x/a). Find mean value for part of curve where x lies between b and a. I have gone thus far y=b[1cos(2pi x/a)/2]/2 Integral y from a to b=b/2(ba)ab/4pi[sin(2pi b/a)sin2pi) MV=b/2[ab sin(2pi b/a)]/(ba) Ans given is b/a. I


Let P be the point on the unit circle U that corresponds to t. Find the coordinates of P and the exact values of the trigonometric functions of t, whenever possible. (If there is no solution, enter NO SOLUTION.) 4pi = ( , ) sin(4pi) = cos(4pi) = tan(pi) =

use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(pi/6), cos(5pi/3) and tan (4pi/3). I know that sin (pi/6) = 1/2 and cos (5pi/30 = 1/2 and

Approximate the equation's solutions in the interval (0,2pi) sin2x sinx = cosx 2cos(x) (1/2sin^2x) = 0 Then I got 3pi/2, pi/2, pi/6 and 5pi/6 Then I substituted 03 and got 3pi/2 , 5pi/2 , 9pi/2 , pi/2, pi/6, 7pi/6, 13pi/6 , 19pi/6 , 5pi/6 , 11pi/6 ,

What values for theta(0 <= theta <= 2pi) satisfy the equation? 2 sin theta cos theta + sqrt 3 cos theta = 0 a. pi/2, 4pi/3, 3pi/2, 5pi/3 b. pi/2, 3pi/4, 3pi/2, 5pi/3 c. pi/2, 3pi/4, 3pi/2, 5pi/4 d. pi/2, pi/4, 3pi/2, 5pi/3 I have spent hours on this

Find complete length of curve r=a sin^3(theta/3). I have gone thus (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int Sqrt[sin^4(t/3){(sin^2(t/3)+cos^2(t/3)}]dt=a Int

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables sin pi/6

find the trigonometric form of 1212(square root)3i a. 24(cos2pi/3 + isin 2pi/3) b. 24(cos4pi/3 + isin 4pi/3) c. 12(cos 4pi/3 + isin 4pi/3) d. 12(cos12pi/3 + isin 2pi/3) e. 12(squareroot) 2 (cos4pi/3 + isin 4pi/3)

1. Use halfangle identity to find the exact value of cos165. MY ANSWER: (1/2)sqrt(2+sqrt(3)) 2. Solve 2 sin x + sqrt(3) < 0 for 0<= x<2pi. MY ANSWER: (4pi/3)< x < (5pi/3) 3.Write the equation 2x+ 3y5=0 in normal form? (2sqrt(13)/13)x 

Find all solutions of the equation. Leave answers in trigonometric form. x^51024=0 I got 4(cos tehta + i sin tehta), tehta = 0, 2pi/5, 4pi/5, 6pi/5, 8pi/5 is this right


Find the exact value of csc 4pi/3 What I have determined thus far: 4pi/3 = 60 degrees sin = square root of 3/2

Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^24csc=1 My attempt: 3(cos^2/sin^2)4/sin=1 3(cos^2/sin^2)  4sin/sin^2 = 1 3cos^2 4sin =sin^2 3cos^2(1cos^2) =4sin 4cos^2 1 =4sin Cos^2  sin=1/4 (1sin^2)  sin =1/4

i did this problem and it isn't working out, so i think i'm either making a dumb mistake or misunderstanding what it's asking. A particle moves along the x axis so that its velocity at any time t greater than or equal to 0 is given by v(t) = 1 

Teach me how to express 5sqrt3  5i in polar form please. I don't want you to do the work for me. Just show me the steps I need to do the work properly on my own. Otherwise I will not pass this class or the exam when I enter college, and I do not want to

1. Determine whether Rolle's Theorem applied to the function f(x)=((x6)(x+4))/(x+7)^2 on the closed interval[4,6]. If Rolle's Theorem can be applied, find all numbers of c in the open interval (4,6) such that f'(c)=0. 2. Determine whether the Mean Value

Find all the solutions of the equation in the interval (0,2pip) sin(x + pi/6)  sin(x pi/6) = 1/2 I am only stuck on the last part. I have 2sinx(sqrt3/2) = 1/2 Does the 2 cancel out with the sqrt 3/2. I am not sure what to do.

Find all the solutions of the equation in the interval (0,2pip) sin(x + pi/6)  sin(x pi/6) = 1/2 I am only stuck on the last part. I have 2sinx(sqrt3/2) = 1/2 Does the 2 cancel out with the sqrt 3/2. I am not sure what to do.

3. find the four angles that define the fourth root of z1=1+ sqrt3*i z = 2 * (1/2 + i * sqrt(3)/2) z = 2 * (cos(pi/3 + 2pi * k) + i * sin(pi/3 + 2pi * k)) z = 2 * (cos((pi/3) * (1 + 6k)) + i * sin((pi/3) * (1 + 6k))) z^(1/4) = 2^(1/4) * (cos((pi/12) * (1 +

Find all solutions of the equation in the interval [0,2pi) 2 cos^2 xcos x = 0 2cos^2 + cosx + 0 (x+1/2) (x+0/2) (2x+1) (x+0) 1/2,0 2Pi/3, 4pi/3, pi/2, 3pi/2 my teacher circled pi/2 and 3pi/2 What did I do wrong? I don't understand...

what are the indicated powers of these complex numbers: a. (2 – 3i )^2 b. (3 + 4i )^3 c. [2 cis(300°)]^5 d. ( cos (4pi/3) + i sin (4pi/3)) ^4


Find all solutions of the equation in the interval [0, 2pi). Show all work. sin(x+(pi/6))sin(x((pi/6))=1/2

Find an equation of a line tangent to y = 2sin x whose slope is a maximum value in the interval (0, 2π] I believe the equation is y=2x4pi. How is the bvalue 4pi?

Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the xaxis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now,

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 seconds. The maximum rate of air flow into the lungs is about 0.5 L/s. This explains, in part, why the function

refer to the graph of y=sin(x) or cos(x) to find the exact values of (x) in the interval [0,4pi]that satisfy the equation. 4sin(x)=4

Can I please get some help on these questions: 1. How many solutions does the equation,2sin^2 2 θ = sin2θ have on the interval [0, 2pi]? 4? ...what about 4cos2θ = 8cos^2 2θ? 2. True or False: sin^2 4x = 1 has 8 solutions on the interval

1)Find the amplitude of y=6cos4theta A)3/2 B)6 C)4 D)pi/2 I chose B 2)Find the period of y=tan5theta A)10pi B)2pi/5 C)5pi D)pi/5 I chose D 3)Find the phase shift of y=sin(theta3pi/4). A)3pi/4 B)3pi/4 C)4pi/3 D)4pi/3 I chose A 4)Find the vertical shift

Can someone please check my answers and help me with the last question! 1. Solve sin2xcos2x = 4sin2x on the interval [0, 2pi] 0, pi, 2pi? 2. Exact value of sin(pi/12)  sin(5pi/12) root3/4? 3. Using factorial notation, 0! = 1 False? 4. Find the area of the

Find all relative extrema and points of inflection of the function: f(x) = sin (x/2) 0 =< x =< 4pi =< is supposed to be less than or equal to. I can find the extrema, but the points of inflection has me stumped. The inflection point is (2pi,0) but

I need to find the exact solutions on the interval [0,2pi) for: 2sin^2(x/2)  3sin(x/2) + 1 = 0 I would start: (2sin(x/2)1)(sin(x/2)1) = 0 sin(x/2)=1/2 and sin(x/2)=1 what's next? Ok, what angle has a sin equal to say 1/2 sin (x/2)=1 arc sin (1) = x/2


Find all solutions to the equation tan(t)=1/tan (t) in the interval 0<t<2pi. Solve the equation in the interval [0, 2pi]. The answer must be a multiple of pi 2sin(t)cos(t) + sin(t) 2cos(t)1=0 Find all solutions of the equation 2cos3x=1

2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= cos(x) 2sin(x) = 1 sin(x) = 1/2 at

An Arc of length 6 cm subtends a 80 degree angle in a circle. What is the radius of the circle? Also what is the area of that sector? What I have so far: S=R*80 degree S= R*4pi/9 6 cm= r* 4pi/9 R=6/4pi/9 R= 6*9/4pi R=54/4pi HELP!

Perform the operation shown below and leave the result in trigonometric form. [6(cos 5pi/6 + isin 5pi/6)] [3(cos 4pi/5 + isin 4pi/5)]

Find the coterminal angles for 8pi/3. I found one: 8pi/3  2pi= 2pi/3 My textbook says that I should add subtract 4pi to find the other one and I'm very confused as to how you know what to add/ subtract.

cos^2(x) + sin(x) = 1  Find all solutions in the interval [0, 2pi) I got pi/2 but the answer says {0, pi/2, pi} Where does 0 and pi come from for solutions? When simplifying I just get sin(x)=1

integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=cos(t) i integral sin(t)e^(it)dt= e^(it)cos(t)+i*integral cost(t)e^(it)dt do integration by

Find all solutions of cos (x) + 1/2 sec (x) = 3/2 in the interval (2pi, 4pi) (Leave your answers in exact form and enter them as a commaseparated list.)

I am given arcsin (sin 4pi) do the arc sin and sin cancel out? How do we solve this?

Find all solutions in the interval [0,2pi]. sin 2x + sin x = 0


Evaluate. 1. sin^1(1/2) 2. cos^1[(root 3)/2] 3. arctan[(root3)/3] 4. cos(arccos2/3) 5. arcsin(sin 2pi) 6. sin(arccos 1) I got these values as my answers: 1. pi/6 2. 5pi/6 3. pi/6 4. 2/3 5. 2pi 6. 0 Can someone please tell me if they are right? thank

cos/sin use 2npi and tan uses npi, but how do you know when to add 2npi or npi to the solution of the equation?

Hello! Can someone please check and see if I did this right? Thanks! :) Directions: Find the exact solutions of the equation in the interval [0,2pi] cos2x+sinx=0 My answer: cos2x+sinx=cos^2xsin^2x+sinx =1sin^2xsin^2x+sinx =2sin^2x+sinx+1=0

please help me with some questions I skipped on a review for our test coming up? solve 57 on the interval 0 greater than or equal to x less than or equal to 2pi. 5. sin x=sqrt3/2 6. cos x=1/2 7. tan x=0  14. what is the exact value of

Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^1 1/2) Sin^1 (sin 7pi/6)

y= sin x/2, 0 less than equal to x less than equal to 4pi... the question says state the amplitude and period for each equation and graph it over the indicated interval

Find all solutions to the following equation on the interval 0<=x<=2PI 8cos^2(X)sin^2(X) + 2cos^2(X)  3 = 0 There are 8 solutions. If somebody could show me how to do it and not give me the answers, that would be great.

Prove that sin 13pi/3.sin 8pi/3+cos 2pi/3.sin 5pi /6=1/2.

Find the exact solutions of the equation in the interval [0,2pi). sin(x/2)+cos(x)=0

Directions: Find all solutions of the equation in the interval (0, 2pi) sin x/2=1cosx


Find all solutions on the interval (0, 2pi) of the equation: 2(sin^2)t3sint+1=0 how do you get this one started?

Find all solutions of the equation in the interval [0,2pi] algebraically. sin^2x + cosx + 1 = 0

Hi! Okay so I started to attempt this math problem; 3cot^2x1=0. However, I'm a little stuck. My teacher wants me to find the Location on The Unit Circle, Period, and General Solution. Can someone check what I have and help me with the rest? 3cot^2x1=0

Find all solutions of the given equation in the interval [0, 2pi) cos x/2  sin x = 0 Hi, I am struggling with this question. Can anybody help me please? Thanks!

1)Write the equation sin y= x in the form of an inverse function. A)y=Sin1x B)x=Sin1y C)y=sin1x D)y=Sinx I chose A 2)Solve y=Arcsin1/2 A)5pi/6 B)5pi/6 C)pi/6 D)pi/6 I chose D 3)Find the value of Sin1(1/2) A)30 degrees B)30 degrees C)150 degrees

Consider the function f(x)=sin(1/x) Find a sequence of xvalues that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin

Consider the function f(x)=sin(1/x) Find a sequence of xvalues that approach 0 such that (1) sin (1/x)=0 {Hint: Use the fact that sin(pi) = sin(2pi)=sin(3pi)=...=sin(npi)=0} (2) sin (1/x)=1 {Hint: Use the fact that sin(npi)/2)=1 if n= 1,5,9...} (3) sin

the number of solutions of sin x= sqrt3/2 for x between 0 and 2pi

Use the halfangle identities to find all solutions on the interval [0,2pi) for the equation cos^2(x) = sin^2(x/2)

Use the halfangle identities to find all solutions on the interval [0,2pi) for the equation sin^2(x) = cos^2(x/2)


I have no idea how to do these type of problems. Problem Solve each equation on the interval 0 less than or equal to theta less than 2 pi 42. SQRT(3) sin theta + cos theta = 1  There is an example prior to the

I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect. 1) a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos

how many solutions does the equation sin(5x)=1/2 have on the interval [0,2pi]?

hey, i would really appreciate some help solving for x when: sin2x=cosx Use the identity sin 2A = 2sinAcosA so: sin 2x = cos x 2sinxcosx  cosx = 0 cosx(2sinx  1)=0 cosx = 0 or 2sinx=1, yielding sinx=1/2 from cosx=0 and by looking at the cosine graph, we

These questions are related to de moivre's theorem: z^n + 1/z^n = 2cosntheta z^n  1/z^n = 2 isin ntheta 1. Express sin^5theta in the form Asintheta + Bsin3theta + Csin5theta and hence find the integral of sin^5theta. 2. Express sin^6theta in multiples of

find all solution to the equation 3 cos(x+4)=1. in the interval of 0<x<2pi This is what I got: arccos (1/3)+4 but I cant figure the rest out Solve the following equation in the interval [0, 2pi]. (sin(t))^2=1/2. Give the answer as a multiple of pi.

Evaluate the following expressions. Your answer must be an angle in radians and in the interval [(pi/2),(pi/2)] . (a) sin^(1)(0) = (b) sin^(1)((sqrt3)/2) = (c) sin^(1)(1/2) =

find all solutions in the interval [0,2 pi) sin(x+(3.14/3) + sin(x 3.14/3) =1 sin^4 x cos^2 x Since sin (a+b) = sina cosb + cosb sina and sin (ab) = sina cosb  cosb sina, the first problem can be written 2 sin x cos (pi/3)= sin x The solution to sin x =

I need to find all solutions of the given equations for the indicated interval. Round solutions to three decimal places if necessary. 1.) 3sin(x)+1=0, x within [0,2pi) 2.) 2sin(sq'd)(x)+cos(x)1=0, x within R 3.) 4sin(sq'd)(x)4sin(x)1=0, x within R 4.)

With Taylor/Maclaurin polynomials Use the Remainder Estimation Theorem to find an interval containing x = 0 over which f(x) can be approximated by p(x) to three decimalplace accuracy throughout the interval. f(x) = sin x p(x) = x  1/6 * x^3 The book


Approximate the equation's soultions in the interval (o, 2pi). If possible find the exact solutions. sin 2x sinx = cosx I do not know where to start.

Approximate the equation's soultions in the interval (o, 2pi). If possible find the exact solutions. sin 2x sinx = cosx I do not know where to start.

Jamie is forming a cylinder out of two circles and a rectangle. The area of each circle is 4 pi. The diameter of each circle is 4 cm. The height of the rectangle is 6 cm. Which shows how Jamie could calculate the surface area of the cylinder? a. 2(4pi)+

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a commaseparated list.) 10 sin^2 x = 3 sin x + 4; [0, 2π)

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a commaseparated list.) 10 sin^2 x = 3 sin x + 4; [0, 2π)

Use inverse trigonometric functions to find the solutions of the equation that are in the given interval, and approximate the solutions to four decimal places. (Enter your answers as a commaseparated list.) 10 sin^2 x = 3 sin x + 4; [0, 2π)

1) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number. cos 12° cos 18° − sin 12° sin 18° And Find its exact value. 2) Use an Addition or Subtraction Formula to write the expression as a

can I please have help with these 3 questions? 1. Solve this equation graphically on the interval [0, 2ð]. list the solutions. sin(2x)1=tan x 2. solve sin x cos x= sqrt3/4 3. solve tan^2 x3tan x+2=0 thank you! show step by step please.

Find the exact solutions of the equation In The interval.. Sin 2x sin x=0

In the equation 4pi^2/G/p^2 times a^3, what is the value of 4pi^2? Is it 39.47? or 157.913


Solve for x in the interval [pi,0] a) sin^2x = 3/4 I know that you have +root3/2 and root3/2 and the positive one gives you an error when doing the inverse of sin, but im confused about the root3/2. I found that one of the answers of x is pi/3 (60

Find the area in the first quadrant bounded by the arc of the circle described by the polar equation r = (2 sin theta)+(4 cos theta) A. 5pi/2 B. (5pi/2)+4 C. 5pi D. 5pi + 8

The graph of f(x), a trigonometric function, and the graph of g(x) = c intersect at n points over the interval 0 <= x <= 2pi. There are m algebraic solutions to the equation f(x) = g(x), where m > n. Which of the following functions are most

i'm having trouble evaluating the integral at pi/2 and 0. i know: s (at pi/2 and 0) sin^2 (2x)dx= s 1/2[1cos(2x)]dx= s 1/2(xsin(4x))dx= (x/2) 1/8[sin (4x)] i don't understand how you get pi/4 You made a few mistakes, check again. But you don't need to

Find all x, 4pi < x < 6pi, such that [cos(x/3)]^4 + [sin(x/3)]^4 = 1 PLEASEEE HELPP! :(