Trigonometry Questions and Answers

Verify that the equation is an identity. sin 2D cos 2D = sin 2D-4 sin ³D cos D To verify the identity, rewrite the more complicated side of the equation so that it is identical to the simpler side. Choose the correct transformations and transform the expression at each step. sin 2D-4 sin ³Dcos D=

Use a half-angle identity to find the exact value. cos 67.5°

Use a half-angle identity to find the exact value. cos 112.5° cos 112.5° = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Use the given information to find (a) sin (s+t), (b) tan (s+t), and (c) the quadrant of s+ t. sin s=1/4 and sint= -3/4 in quadrant II and t in quadrant IV (a) sin (s+t)= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Write the expression as an algebraic expression in u, u>0. tan( cos^-1( 2/√u^2+4)) tan( cos^-1( 2/√u^2+4))= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Find a simplified expression for cos( sin^-1 (y/6)) Find a simplified expression for cos( sin^-1 (y/6))

Find the exact value of the expression. sin[sin-1 5/13 + cos -1(-4/5)] sin[sin-1 5/13 + cos -1(-4/5)]= (simplify your answer,including any radicals.)

Fill in the blank to complete the fundamental identity. sin (-θ)=

Use the given information to find (a) sin (s+t), (b) tan (s + t), and (c) the quadrant of s+ t. cos s=4/5 and cost=8/17 s and t in quadrant IV (a) sin (s+t) =

Use the given information to find (a) sin (s+t). (b) tan (s+t), and (c) the quadrant of s+t. sin s=2/3 and sint=-1/3, in quadrant II and t in quadrant IV (a) sin (s+t)=

Give the equation y=4tan(8x+32) period= horizontal shift= units to the

On the interval [0, 2π) determine which angles are not in the domain of the tangent function, f(0) = tan(0) What angles are NOT in the domain of the tangent function on the given interval?

Find the exact value of the following expression. Write the answer as a single fraction. Do not use a calculator. sin23π/4cos5π/6+cos23π/4sin5π/6 sin23π/4cos5π/6+cos23π/4sin5π/6 (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Find the exact value of the expression. Do not use a calculator. tan π/3 /2 + 1 /sec π/6 tan π/3 /2 + 1 /sec π/6 = (Type an exact answer, using radicals as needed. Simplify your answer.)

Use a calculator to find the value of the acute angle θ in radians. tan θ = 0.4173

Find the exact value of each of the six trigonometric functions of θ, if (9, -3) is a point on the terminal side of angle θ. ... sin θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cos θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) tan θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) csc θ = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) sec θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.) cot θ= (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Virginia is flying a Cessna and is descending at a 7° angle towards a runway. If she can see a gorge behind her at a 50° angle that is 500 feet away from the runway, how much further does she have to fly until she lands? Round to the nearest tenth.

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth. cos 33°

A pole that is 2.7 m tall casts a shadow that is 1.8 m long. At the same time, a nearby tower casts a shadow that is 44.25 m long. How tall is the tower? Round your answer to the nearest meter.

A pole that is 3 m tall casts a shadow that is 1.54 m long. At the same time, a nearby building casts a shadow that is 44.5 m long. How tall is the building? Round your answer to the nearest meter.

A pole that is 3.2 m tall casts a shadow that is 1.27 m long. At the same time, a nearby tower casts a shadow that is 49.5 m long. How tall is the tower? Round your answer to the nearest meter.

List 2 angles (in radian measure) with 0≤θ<2π for which the cosine of each is -√3/2 .

Given the equation y = 2 sin(7(x + 5)) + 4 The amplitude is: The period is: The horizontal shift is:____units to the Select an answer The midline is: y =

Given the equation y=4 sin (4π/3 x +8π) +7 The amplitude is: The period is: The horizontal shift is:___units to the Select an answer The midline is: y =

Given the equation y=5 sin(7x + 14) + 4 The amplitude is: The period is: The horizontal shift is:___units to the Select an answer The midline is: y =

Sketch a graph of the function f(x) = cos(x).

Verify the identity: 2 csc A = sin A / 1 + cos A + 1 + cos A / sin A

Verify the identity: cos A = sin² A/1- cos A - 1

Verify the identity: cos (2A)/1 + sin (2A) = cot A -1/cot A+1

Find two values of θ, 0≤θ<2π, that satisfy the following equation. tan θ= 1

Find the reference angle for the angle 37π /6

Let 0 be an angle in standard position. Name the quadrant in which θ lies. tan > θ, sin θ> 0 The angle θ lies in which quadrant? II i IV

Determine the amplitude, period, any vertical translation, and any phase shift of the given graph. y=-2 cos(x/5 + π/5) The amplitude is

___ =sin 2θ and ____= tan θ/2 given and cot = 15/8 and terminates in Quadrant III.

A coin is tossed twice. Let E be the event "the first toss shows heads" and F the event "the second toss shows heads". (a) Are the events E and F independent? Input Yes or No: (b) Find the probability of showing heads on both tosses. Write your answer as a reduced fraction. Answer:

In Problems 39-56, use the even-odd properties to find the exact value of each expression. Do not use a calculator. 47. tan (-π/4) 48. sin (-π) 49. cos (-π/4)

A tower that is 101 feet tall casts a shadow 106 feet long. Find the angle of elevation of the sun to the nearest degree.

If f(θ) = 2 sin θ-sin 2θ, find f(π/6). Do not use a calculator and express each exact value as a single fraction. f(π/6)=

People who believe in biorhythms claim there are three cycles that rule our behavior - the physical, emotional, and mental. Each is a sine function of a certain period. The function for our emotional fluctuations is E = sinπt/18 (Equation may not be based on actual studies.) where t is measured in days starting at birth. Emotional fluctuations, E, are measured from 1 to 1, with 1 representing peak emotional well-being, 1 representing the low for emotional well-being, and 0 representing feeling neither emotionally high nor low. a. Find E corresponding to t = 63, 72, 81, 90, and 99. Describe what you observe. b. What is the period of the emotional cycle? a. Find E corresponding to t = 63.

Use a calculator to approximate the following to 6 decimal places: csc 52°12′07"

3. For y = -1 b + cos x with 0 ≤ x ≤ 2π and 2 ≤ b ≤ 6, where does the lowest point of the graph occur? What happens to the graph as b increases?

A radio tower is located. 350ft from a building. from a window in the building, a person determines that the angle of elevation to the top of tower is 38° and that angle of depression to bottom of tower is 25°. How tall is the tower?

IF sin(0) = -4/5, and 0 is in IV, then find quadrant (a)Cos (0)= (b) tan(o) = (c) sec (0) = (d) csc (0) = (e) cot (o)=

A 16-ft ladder leans against a building so that the angle between the ground and ladder is 99. How high does ladder reach on building? Ft

Use a calculator to find the following values: sin(0.3) cos(0.3) tan(0.3)

If cos(θ)=-1/8 and θ is in the 3rd quadrant, find the exact value for sin(θ) sin(θ) =

Find an angle with 0° <θ<360° that has the same: Sine as 20°:θ= degrees Cosine as 20°: θ = degrees

If θ=-5π/4,then sin (θ) = cos(θ) Give exact values. No decimals allowed!

If θ=4π/3,then sin(θ) = cos(θ) = Give exact values. No decimals allowed!

Find an angle with 0° < θ < 360° that has the same: Sine function value as 260° θ = degrees Cosine function value as 260° θ = degrees