Trigonometry Questions and Answers

1. If tan x = 4 then tan(-x) = 2. If sin x = 0.7 then sin(-x) = 3. If cos x = 0.5 then cos(-x)= 4. If tan x 0.5 then tan(π + x) =

If cos(θ)= - 2|5 and is in the 2nd quadrant, find sin(θ)

For each part, type your answer in as a fraction. Do not use a decimal or round your answers. If sin(x)=-3/5 ,then csc(x)= If cos(x)=2/3 ,then sec(x)= If tan(x) = 7, then cot(x) =

If cos(θ)=3/8 and θ is in the 1st quadrant, find sin(θ) sin θ

Given that the point (14, 48) is on the terminal side of an angle, θ, find the exact value of the following: sin (θ)= cos(θ)= tan (θ)= csc (θ)= sec (θ)= cot (θ)=

Given angle A=47.03925° and angle B=75°27'30", then Angle A= Sec. and Angle B= Deg.. Min.___ Decimal Deg.

Express the following as a function of a single angle. tan 60° + tan 45º/1- tan 60° tan 45° tan[ ? ]°

Solve for x where 0≤x≤π cos²x-sin²x = 1/2

Express the following as afunction of a single angle. tan 145° + tan 85°/1- tan 145° tan 85°

Simplify. 1 - tan²x/ 1 + tan²x

Calculate the exact value of sin 105° using the half-angle formula. Rationalize the denominator if necessary.

Express the following as a function of a single angle. cos 40° cos 70° + sin 40° sin 70° cos[?]°

Find sin 255° without using a calculator. -√2-√[?]/[ ]

Express the following as a function of a single angle. tan(-34°)+tan(-110°)/1-tan(-34°) tam(-110°)

If θ is in the first quadrant and cos θ = 3/5 , what is sin(1/2 θ)? Determine your answer without using a calculator. Rationalize the denominator if necessary. 19 sin (1/2θ) = [?]

A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 43° and that the angle of depression to the bottom of the tower is 21°. How tall is the tower? feet

A 37-ft ladder leans against a building so that the angle between the ground and the ladder is 85° How high does the ladder reach on the building? ft

Suppose is an angle such that cos(θ)=-2/7 If π <θ< 2π, then cos(θ/2)= and sin(θ/2)=

What is the total change of f(x), if f'(x) = cos(3x), over the interval [0, π]? -1 0 √2/2 1

Find the value of s in the interval [0,π/2] that satisfies the given statement. tan s=0.8367 S =

Use the cofunction identities to evaluate the expression without the aid of a calculator. sin² 15⁰+ sin² 75⁰

sketch two periods of the graph of the given function. Be sure that the "fab five" points/places clearly represented on each graph. y = 1- tan(π /10 x)

With the given set of components, find R and θ Rx = -723, Ry= -201

Determine the amplitude, period, and displacement of the given function. Then sketch the graph of the function. y = 2win (x-1) The amplitude is The period is The displacement is

Write the function of the form y sin bx corresponding to the given period. Period: 1 Fill in the correct value for b.

With the given set of components, find R and 8. R=-718, R=-212

Find R and given the components R, = 15.11 and R, = 7.31. R=

Find the exact value. sin(4π/3) sin(4π/3)= (Type an integer or a fraction. Type an exact answer, using radicals as needed.)

Find a calculator approximation to four decimal places for the circular function value. sin 2.8843 sin 2.8843≈ (Round to four decimal places as needed.)

Find the exact value of csc(π/3) csc(π/3)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Find the exact function value. cos 3π/2 cos 3π/6= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Find the exact function value. sec π/6 sec π/6= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Solve within invertal 0 < t < 2π. a) Let w = sin(t) so we can rewrite the equation as: b) Use Quadratic Formula to solve for w. That means: Write the negative root first. sin(t)= sin² (t) 1 = -6 sin(t) and sin(t) = c) Solve each equation for t within invertal [0, 2pi) using trig inverses: t= Round answers to 4 decimal places.

Find the exact value of sin(- π/6 radians) a. -√3/2 b. -1/2 c. -√2/2 d. -1 select one : A. a B. b C. c D. d

Find the domain, period, range, and amplitude of the cosine function. y = -6 cos 4x a. domain =-1/2≤ x ≤1/2-; period = 6; range: -6 ≤ y ≤ 6; amplitude=1/2 b. domain=all real numbers; period=1/2 π; range: -6 ≤ y ≤ 6; amplitude = 6 c. domain = all real numbers; period=1/2-; range: -6 ≤ y ≤ 6; amplitude = -6 d. domain =-1/2≤ x ≤1/2-; period = 6; range: -6 ≤ y ≤ 6; amplitude=1/2

Solve the equation below in the interval from 0 to 2π. Round to the nearest hundredth. cos π/2 t = -1/2 Choose the correct answer below. A. t-1.23, 2.57, 5.23 B. t-1.23, 2.75, 5.23 C. t=1.33, 2.67, 5.33 D. t=1.33, 2.76, 5.33

Solve the equation below in the interval from 0 to 2. Round to the nearest hundredth. 8 cos π/3 t=5 Choose the correct answer below. A. t=0.92, 5.10 B. t=0.86, 5.14 C. t=0.92, 5.20 D. t=0.86, 5.24

solve the triangle c= 20 b=16 a=? f find Sin theta Cos Tan Csc sec cot

The measure of an angle is standard position is given. Find the exact values of cos 0 and sin 8. Choose all that apply. 2π/3 radians Select one or more: a. cosine is √3/2 b. cosine is -1/2 c. cosine is -√2/2 d. sine is √3/2 e. sine is -1/2 f. sine is √2/2

The measure of an angle in standard position is given. Find the exact values of cos 0 and sin 0. Choose all that apply. π/6 radians Select one or more: a. cosine is √3/2 b. cosine is 1/2 c. cosine is √2/2 d. sine is √3/2 e. sine is 1/2 f. sine is √2/2

The measure of an angle is standard position given. Find the exact values of cos 0 and sin 8. Choose all that apply. 5π/4 radians Select one or more: a. cosine is √3/2 b. cosine is -1/2 c. cosine is -√2/2 d. sine is -√3/2 e. sine is -1/2 f. sine is -√2/2

Your are still standing 120 feet away from the spot where James Bond blasted off in his jet pack in exam 2. Unfortunately, enemy agents cut one of his fuel lines just before take off and he has exhausted his fuel supply. You are now mesmerized by his free-fall descent and he plummets straight downward back to earth.. From your viewing point over a short span of time, Mr. Bond's angle of elevation decreases from 67° to 47°. To the nearest foot, how far did 007 fall during this time? (Don't worry, he was able to deploy a hidden parachute at the last minute and survived the fall without injury)

Graph the trigonometric function.y=-1/2cos 2x Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.

J.J. has her treadmill set to adjust the slope from 0° to 12º and back to 0° over a 20 minute period. A function that models the slope of her treadmill is y = 6sin(p/10(x - 5)) + 6 x is in minutes and y is the degree of the slope. Show steps to find the two values at which the slope is 8° within the first 20 minute period.

Use the information given below to find tan (a + b). sin a=15/17, with a in quadrant I lan B=4/3 with b in quadrant III Give the exact answer, not a decimal approximation. tan (a + b) =

Find 0 for 0° ≤θ<360°. sin θ=-0.8162 θ=_________

In a certain city, the number of hours of sunlight on the summer solstice is 15.562 and the number of hours of sunlight on the winter solstice is 8.394. Answer the following questions. Assume that summer solstice occurs on the 172nd day of the year, and that there are 365 days until the next summer solstice. (a) Find a sinusoidal function of the form y = A sin (ωx-φ) + B that fits the data. A =

Name the set of all angles measured in radians such that the condition holds true: a) csc = -2: b) cot = √3: c) cos :=√2/2

Which angle is not in the set of all angles described by19pi/10+ 2πk? 19 pi/10 21pi/10 -39pi/10 all choices here are coterminal pi/10

Find the exact value of t given sint = −1 & t = [0, π].