# Trigonometry

Trig
cos 13 pi = ?

math trig
Solve for x if 3sin2x - 3sinx = 2 - 4cosx 0<x<180

trig
If sinx=3 cosx, then what is sinx∙cosx?

Trig
Solve, algebraically or with justification (no graphing calculator solutions allowed), the following equation: tan⁡7x-sin⁡6x=cos⁡4x-c​ot⁡7x

Trig
What is the value of tan⁡x given that sin⁡x+cos⁡x=1/5 and π/2<x<π ?

Trig
Algebraically find the value of: 10 cot⁡(cot^(-1)⁡3+cot^(-1)R​89;7+cot^(-1)⁡13+cot^(-1)⁡21​ )

Trig
Write an algebraic expression for the following: sin⁡(arctan⁡〖(x+1)/(x​-1)〗 )

Trig
Prove the identity: (sin⁡(2x-y)+sin⁡y)/(cos̼​9;(2x-y)+cos⁡y )=tan⁡x

trig
The hypotenuse of a right triangle has length 8. The area of the triangle is also 8 units squared. What is the perimeter of the triangle?

trig
what is terminal point of 5pi/4?

trig
A road has a 10% grade (slope). To the nearest degree what is the angle of elevation of the road?

Maths trig
Sketch the graphs of f(x)=3overx+1 and g(x)=-2x-4 on the same set of axes

Maths trig
Sketch the graphs of f(x)=3overx+1 and g(x)=-2x-4

trig
Help with simplest form sin(2pift - pi) + sin(2pift + pi)

trig
A radio transmission tower is 471.0 feet tall. A guy wire is to be attached 6 feet from the top and is to make an angle of 23.1 degrees with the ground? How many feet long should the guy wire be? I am confused on how to find the equation for this problem so that I may work it ...

Trig/ algebra 2
if f(x) = sin4x-cos2x, find f(pi/8)

Trig/Geometry
Wendy spots a pizza delivery car as she is looking down at a 15° angle from the top of her apartment building, which is 145 ft tall. How far away is the car from the base of the building? Round to the nearest hundredth. A. 45.98 ft B. 3.56 ft C. 38.85 ft D. 68.78 ft I keep ...

trig
An airplane is heading north at an airspeed of 500 km/hr, but there is a wind blowing from the northwest at 50 km/hr. how many degrees off course will the plane end up flying, and what is the plane's speed relative to the ground? So here is my work... 50cos(45)+500= 535.355 ...

Trig
Find sin2theta, cos2theta, and tan2theta for costheta = -12/13 in pi < theta < 3pi/2. My answers: 20111/24336 for tan2theta. 144/169 for cos2theta -120/338 for sin2theta

Trig
For 90<theta<180, cos theta = -(5/13). Which is sin theta? 1. - sqrt 13/9 2. - sqrt 9/13 3. sqrt 9/13 4. sqrt 13/9 3?

Trig
Which is cos2 theta if sin theta = -2/sqrt13 and 180 < theta < 270? 1. -(13/5) 2. -(5/13) 3. 5/13 4. 13/5 3?

algebra 2 and trig
The scores on a chemistry test are normally distributed. Approximately 95 percent of the scores fell between 78 and 92. What is the standard deviation for this distribution?

Trig
Solve each equation for the given domain. cos^2 theta + cos theta - 1 = 0 for 0-180.

Trig
Solve the equation for the given domain. 4cos^2 θ = 1 for 0 to 360 degrees. I get 60, 120, 240, and 300. Are these correct? If so, how would I represent them with some sort of expression?

Trig Identities
Prove the following identities: 13. tan(x) + sec(x) = (cos(x)) / (1-sin(x)) *Sorry for any confusing parenthesis.* My work: I simplified the left side to a. ((sinx) / (cosx)) + (1 / cosx) , then b. (sinx + 1) / cosx = (cos(x)) / (1-sin(x)) I don't know how to verify the rest.

Trig identities
Sin x/[1-cos(-x)] = csc x + cot x Please Verify the Identity. I have been going in circle with this one... Just a hint would be nice. Thank you.

trig
a vertical pole 35 feet high, standing on sloping ground, is braced by a wire which extends from the top of the pole to a point on the ground 25 feet from the foot of the pole. If the pole subtends an angle of 30 degree at the point where the wire reaches the ground, how long ...

Trig
A ladder 35.4 feet long is leaning against an embarkment inclined 62.5 degrees to the horizontal. If the bottom of the ladder is 10.2 feet from the embarkment, what is the distance from the top of the ladder down the embarkment to the ground?

trig
From a certain point, the angle of elevation of the top of the building is 38. From a point 75 feet nearer the building, the angle of elevation is 65. Find the height of the building.

Trig
Two pilots take off from the same airport. Mason heads due south. Nancy heads 23 west of south. After 400 land miles, how far is Nancy from Mason’s route? I think 156.29, but I'm not sure because the question comes in a lesson on sum and difference identities, and ...

Trig
Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) =Sin-3/5 cos-3/5 = -0.46602 HELP ...

Trig
Find each value if sin A = 12/13 with 90 degrees <= A <= 270 degrees and if sin B = -7/25 with -90 degrees <= B <= 90 degrees. sin(A - B) sin(A + B)

Trig
secθsinθ is equivalent to: Ans: tanθ?

trig
2-sec=5+sec

trig
Find the values of sin 0, cos 0, and tan 0ƒáif the angle 0ƒáis in standard position and its terminal side passes through the point (¡V15, 8). Give answers as fractions.

trig
Find the bearing and airspeed for a plane to fly 630 miles due north in 3 hours if the wind is blowing from a direction of 318* and is blowing at 15mph. Approximate the bearing to the nearest degree and the speed to the nearest mile per hour.

trig
Forces of 15 kg and 10 kg act on a point with an angle of 60◦ between the forces. Find the magnitude of the resultant force (to nearest tenth of a kilogram) and the angle (to the nearest degree) the resultant makes with the 15 kg force

Physics
The equation of a transverse wave traveling in a string is given by y(x,t) = 10 cos (π/2)(0.0050x - 8.0t + 0.57), in which x and y are expressed in centimeters and t in seconds. Write down the equation of a wave which, when added to the given one, would produce standing ...

Trig
If tan x = -sq rt3/3 and cos x = -sq rt3/2, the measure of <x is?

Trig
The graph of y-7 cosθ + 24 sinθ would be a sinusoid if it were plotted. What would be the first positive value of θ at which there is a high point?

Trig
Please help with this question: A plane travels a distance of 140 km due west of Vancouver International Airport. It then travels 60 km at a bearing of 340 degrees. How far from the Airport is the plane? Thank you for all your help.

Trig
Can you please help with this trig question: The angle of elevation to the top of a nearby mountain is 46 degrees. After walking 1 km toward the mountain, you determine the angle of elevation to be 68 degrees. How high is the mountain? Thank you for all your help.

Trig
Prove that : (Sin Ө + Cosec Ө)/(Tan Ө+Cot Ө) = Sin Ө + Cos Ө

Precalculus Trig (Geometry)
A rectangular doorway is 38 meters wide and 60 meters high. The doorway is capped with a semi-ellipse that is 13 meters high at its center. Find the height h of the doorway and window 5 meters from the center. From the ellipse equation, I can see that a should be 19 and b ...

Precalculus Trig (Geometry)
A large doorway has the shape of a parabolic arch. The doorway is 20 feet high at the top of the arch and 20 feet wide at the base. At a height of 10 feet above the floor, find the width of the arch. If you start the vertex of the parabola at 0,0, that means the equation ...

trig
Karen earns 43 dollars per week working pt at a bookstore. she makes one dollar more for each book she sells. the amt A, in dollars that Karen earns in a week ifshe sells b books is given in the function A(b) =43 + b how much does she earnin a week if she sells 22 books?

geometry/trig
Initially a fifty foot ladder rests against a wall. As I start to climb it, the ladder slides down, finally stopping such that the ladder touches the wall at a point 8 feet below where it originally touched the wall. During the slide, the base of the ladder slid 16 feet from ...

trig
solve triangle ABC which have angleA=25.25,angleB=60.51 and a=3.82..find c...,find b

trig
if sin23=p,write down the following in terms of P *cos113 *cos23 *sin46 so i draw the diagram an solve for x in terms of P an got 1-p so i don't know how to apply cos113and sin46 in terms of 23 or P but *cos 23 i wrote it as> 1-p/1 wch is 1-p

Calculus
1. integral (x^3 * sqrt(x^2-4)) dx I'm confused on how to start this problem, if I am doing trig substitution.

trig
How do I verify this? Cos^4x-Sin^4x=1-tan^2x/sec^2x

Calculus 2 (Differential Equation)
How would you solve the following problem explicitly? Sqrt(1-y^2) dx - sqrt(1-x^2) dy I separated the x and y terms and got: Integral of 1/sqrt(1-x^2) dx = Integral of 1/sqrt(1-y^2) dy I was wondering how would you take the anti-derivative of each function. I believe we are ...

Trig
An isosceles triangle has legs 4 feet long. If the vertex angle measures 30 degrees, find the length of the base.

trig
If cos A= -6/7, in quadrant 2, determine the exact value of tan 2A I don't understand how to do this?

trig
y= 3 cos(x+pi)-3

trig
A gear with a radius of 32 centimeters is turning at pi/9 radians/sec. What is the linear speed (velocity) at a point on the outer edge of the gear?

calculus trig substitution
∫ x^3 √(x^2+9) dx If you work it can you write the steps? I really don't like the way my teacher teaches it. Someone else doing it might help.

trig
a balloon is tethered to the ground by a string 5 m long if the string makes an angle of 65 degrees with the ground how high above the ground is the balloon

trig
A frisbee is thrown within an angular velocity of 360 rpm. If the diameter of the frisbee is 12 inches, how fast does it travel when it hits the ground rolling on the side? round your answer to the nearest mph

Trig
How do you derive this identity? Cos(t)=1-sin^2(t/2)

Trig verifying identities
I am having trouble with this problem. sec^2(pi/2-x)-1= cot ^2x I got : By cofunction identity sec(90 degrees - x) = csc x secx csc-1 = cot^2x Then split sec x and csc-1 into two fractions and multiplied both numerator and denominators by csc and got: sec x csc^2x-1= cot^2x ...

Trig
A pendulum swinging through a central angle of Ts completes an arc of length 6.4 cm. What is the length of the pendulum?

Pre-calc/trig
i think its a or b Which scenario describes periodic behavior? A pendulum swinging back and forth A ball bouncing up and down on the ground The takeoff and landing of a jet plane The path a dolphin swims in the ocean

Precalc+trig
Solve tan(40/90) for the double angle cos(2theta). I know I use the x^2 + y^2 = r^2 formula and cos(2theta) = cos^2theta - sin^2theta. But I don't understand my answer

trig equations
Find all solutions (if they exist)for the given equation on the interval [0,2pi) cos^2x-5sinx+5=0

trig.
If P (x, y) is the point on the unit circle determined by the real number θ, then tan θ= x/y y/x 1/x 1/y

trig
what is the reference angle for 11π/6? how would i do this?

trig with enough info?
Two oil Wells are 4 km and 6 km from the river. The points along the river are 8 km apart. Find the common loading point on the river, using the shortest amount of pipe.

trig
Two oil Wells are 4 km and 6 km from the river. The points along the river are 8 km apart. Find the common loading point on the river.

trig
An airplane is traveling at a speed of 724 km per hour at a bearing of N30°E. If the wind velocity is 32 km per hour from the west, find the resultant speed and direction of the plane.

Trig application
I worked this problem out but I do not fully understand what I am doing. Fire tower A is 30 kilometers due west of fire tower B.. A fire is spotted from the towers, and the bearings from A and B are N 76 degrees E and N 56 degrees W, respectively. Find the distance d of the ...

Trig application
I am having trouble with this question. A privately owned yacht leaves a dock in Myrtke Beach, South Carolina, and heads toward Freeport in the Bahamas at a bearing of S 1.4 degrees E. The yacht averages a speed of 20 knots over the 428-nautical- mile trip. A. How long will it...

Trig application
I have been working on this problem but I am not sure I am doing it right. During takeoff an airplane's angle of ascent is 18 degrees and its speed is 275 feet per second. A. Find the plane's altitude after 1 minute. B. How long will it take for the plane to climb to an ...

I am having a hard time figuring this out. I know I need to find the vertex from the vertex form equation but I am having a hard time figuring out the equation. A caterer will charge a certain club \$20 per member to cater a dinner if 150 members attend. However, the cost per ...

algebra/trig
You need a 100 pounds of two types of candy that cost 50 cents per pound and 75 cents per pound. A.) Verify that your total cost is c(x)=0.50x + 0.75(100-x) thx a ton:)

Trig/Precalc
The system of equations: |z-2-2i|=sqrt(23), |z-8-5i|=sqrt(38) has two solutions z_1 and z_2 in complex numbers. Find (z_1+z_2)/2. My first instinct on this problem was to square each equation given that the square of the magnitude of a complex number is much easier to deal ...

Calculus
Integration with trig functions Integral of [(1-sinx)/cos^2x] dx

Math/Trig
From an observation tower that overlooks a runway, the angles of depression of point A, on one side of the runway, and point B, on the opposite side of the runway are 6 degrees and 13 degrees respectively. The points and the tower are in the same vertical plane and the ...

Calculus
What would an example of a logarithmic function that contains two trig functions within it where you would need to use chain rule and product rule to take derivative look like? How would taking the derivative of the function in its original form look different when using log ...

trig
I am currently taking a trig class. I need help understanding how to solve for sin,cos, and tan in problems which give an angle and a side length or the hypotenus. Any help would be muchly appreciated

Trigonometry
Find cotangent theta given that cosecant theta equals -3.5891420 and theta is in the third quadrant. I was using the trig identity 1+cot^2theta=csc^2theta I wanted to isolate cotangent so I plugged in 1/sin (-3.5891420) and then squared my answer. I then subtracted one from ...

trig
A man is between two tall buildings 8m away from the taller building. If the angle of the top of the building from where he stans bears N 8degrees W for the taller one and N 12degrees E for other. How far is he from the other building if the taller building is 6/5 as to the other

trig
From post C, An airplane and a helicopter travel to different islands.The plane travels.415 km N 60degrees45minutes E to island A. and the helicopter travels to island B at S 19degrees5minutes E for 120 km. what is the distance between tthe two island

Trig
Bob the ranger is atop a fire tower that i son the side of a mountain.The fire tower is 10 meters high and the angle of depression from the top of the tower to the base of the mountain is 48 degrees. The tower creates a 115 degree angle with the mountain. How far up he ...

Trig
How do i solve sinx/cosx(sinx+cosx/sinx×cosx)=secx? I know it's 1/cosx because it equals secx but I don't know how to get there? :^(

trig
two ships p and q left a port at the same time. q sailed on a bearing of 150 while p sailed on the north side of q. after a distance of 8km and 10km by pand q respectively, their distance apart was 12km. find the bearing of p and r

Geometry
I am having trouble with this question. I do not know where to begin. I am in Trig now and we are doing review but I forgot everything that I learned in Geometry. I want to understand how to do this problem. "a picture measures 20 cm by 25 cm. the width of the matting and ...

Trig 4
Can someone break down the meaning of sin, tan, and cos into simpler more understandable terms?

Trig/ English
I need an Acrostic poem for the word "Exponent"

Precalc/Trig
I don't understand how to do these problems: Find two pairs of polar coordinates for each point with the given rectangular coordinates if 0 ≤ θ ≤ 2π. Round to the nearest hundredth, if necessary. 17. (2, -3) Answers: (3.61, 5.30) and (-3.61, 2.16) 19. (a...

Trig/Precalc
Two questions that I would really appreciate some hints on: 1) Circles with centers (2,1) and (8,9) have radii 1 and 9, respectively. The equation for a common external tangent can be written in the form y=mx+b with 0<m. What is b? 2) In triangle ABC, AB=BC, and BD is an ...

Pre-Calc/Trig
write an equation of the conic section: a hyperbola with vertices (0,-6) and (0,6) and asymptotes y=(3/4)x and y=(-3/4)x

trig
an observer at A looks due north and sees a meteor with an angle of elevation of 70 degrees. At the same instant, another observer 30 miles east of A seed the same meteor and approximates its position as N 50 degrees W but fails to note its angle of elevation. Find the height ...

Pre-Calc/Trig
Complete the following for each system that involves one or more quadratic equations: Solve the system algebraically 7y^2-5x^2+20x=3 5x^2+21y^2=209

trig
a guy wire reaches from the top of a 125 meter television transmitter tower to the ground.The wire makes a 63' angle with the ground.Find the length of the guy wire.

Pre-calc/trig
5=log3(x^2+18)

Pre-calc/Trig
For each parabola, find the vertex and focus. x= (1/400)y^2 y= 1/8(x-3)^2-1

Trig/Precalc
So I have two questions that have been puzzling me for quite some time and would really appreciate any help with either of them! (a) There are four positive intergers a, b, c, and d such that 4cos(x)cos(2x)cos(4x)=cos(ax)+cos(bx)+co​s(cx)+cos(dx) for all values of x. ...

Pre-calc/Trig
For each parabola, tell in which direction the graph opens. x= 1/2y^2 y= -1/24x^2

trig
prove that the equation 2sin x cos x +4cos^2 x =1 may be written in the form of tan^2 x -2tan x -3=0