?For the following exercises, use Figure 1 to find the desired quantities.sin

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). \(csc^{2} t = 3\) Text Transcription: csc^2 t = 3

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). \(\cos ^{2} x=\frac{1}{4}\) Text Transcription: cos^2 x = 1/4

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). \(9sin ? ? 2 = 4sin^{2} ?\) Text Transcription: 9sin ? ? 2 = 4sin^2 ?

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). \(1 ? 2tan(?) = tan^{2}(?)\) Text Transcription: 1 ? 2tan(?) = tan^2(?)

For the following exercises, use basic identities to simplify the expression. \(\sec x \cos x+\cos x-\frac{1}{\sec x}\) Text Transcription: Sec x cos x + cos x - 1 / sec x

For the following exercises, use basic identities to simplify the expression. \(sin^{3} x + cos^{2} x sin x\) Text Transcription: sin^3 x + cos^2 x sin x

For the following exercises, determine if the given identities are equivalent. \(\sin ^{2} x+\sec ^{2} x-1=\frac{\left(1-\cos ^{2} x\right)\left(1+\cos ^{2} x\right)}{\cos ^{2} x}\) Text Transcription: sin^2x + sec^2 x - 1 = (1 - cos^2 x) (1 + cos^2 x) / cos^2 x

For the following exercises, determine if the given identities are equivalent. \(tan^{3} x csc^{2} x cot^{2} x cos x sin x = 1\) Text Transcription: tan^3 x csc^2 x cot^2 x cos x sin x = 1

For the following exercises, find the exact value. \(\tan \left(\frac{7 \pi}{12}\right)\) Text Transcription: tan (7? / 12)

For the following exercises, find the exact value. \(\cos \left(\frac{25 \pi}{12}\right)\) Text Transcription: cos (25? / 12)

For the following exercises, prove the identity. \(cos(4x) ? cos(3x)cosx = sin^{2} x ? 4cos^{2} x sin^{2} x\) Text Transcription: cos(4x) ? cos(3x)cosx = sin^2 x ? 4cos^2 x sin^2 x

For the following exercises, prove the identity. \(cos(3x) ? cos^{3} x = ? cos x sin^{2} x ? sin x sin(2x)\) Text Transcription: cos(3x) ? cos^3 x = ? cos x sin^2 x ? sin x sin(2x)

For the following exercise, simplify the expression. \(\frac{\tan \left(\frac{1}{2} x\right)+\tan \left(\frac{1}{8} x\right)}{1-\tan \left(\frac{1}{8} x\right) \tan \left(\frac{1}{2} x\right)}\) Text Transcription: tan (1/2 x) + tan (1/8 x) / 1 - 8 tan(1/8 x) tan (1/2 x)

For the following exercises, find the exact value. \(\cos \left(\sin ^{-1}(0)-\cos ^{-1}\left(\frac{1}{2}\right)\right)\) Text Transcription: cos (sin^-1 (0) - cos^-1 (1/2))

For the following exercises, find the exact value. \(\tan \left(\sin ^{-1}(0)+\sin ^{-1}\left(\frac{1}{2}\right)\right)\) Text Transcription: tan (sin^-1 (0) + sin^-1 (1/2))

For the following exercises, find the exact value. Find sin(2?), cos(2?), and tan(2?) given \(\cos \theta=-\frac{1}{3}\) and ? is in the interval \(\left[\frac{\pi}{2}, \pi\right]\) Text Transcription: cos ? = - 1/3 [?/2, ?]

For the following exercises, find the exact value. Find sin(2?), cos(2?), and tan(2?) given \(\sec \theta=-\frac{5}{3}\) and ? is in the interval \(\left[\frac{\pi}{2}, \pi\right]\) Text Transcription: sec ? = - 5/3 [?/2, ?]

For the following exercises, find the exact value. \(\sin \left(\frac{7 \pi}{8}\right)\) Text Transcription: sin (7?/8)

For the following exercises, find the exact value. \(\sec \left(\frac{3 \pi}{8}\right)\) Text Transcription: sec (3?/8)

For the following exercises, use Figure 1 to find the desired quantities. sin(2?), cos(2?), tan(2?), sin(2?), cos(2?), and tan(2?)

For the following exercises, use Figure 1 to find the desired quantities. sin \(\left(\frac{\beta}{2}\right)\), cos \(\left(\frac{\beta}{2}\right)\), tan \(\left(\frac{\beta}{2}\right)\), sin \(\left(\frac{\alpha}{2}\right)\), cos \(\left(\frac{\alpha}{2}\right)\), and tan \(\left(\frac{\alpha}{2}\right)\) Text Transcription: (?/2) (?/2)

For the following exercises, prove the identity. \(\frac{2 \cos (2 x)}{\sin (2 x)}=\cot x-\tan x\) Text Transcription: 2cos(2x) / sin(2x) = cot x - tan x

For the following exercises, rewrite the expression with no powers. \(cos^{2} x sin^{4}(2x)\) Text Transcription: cos^2 x sin^4(2x)

For the following exercises, rewrite the expression with no powers. \(tan^{2} x sin^{3} x\) Text Transcription: tan^2 x sin^3 x

For the following exercises, evaluate the product for the given expression using a sum or difference of two functions. Write the exact answer. \(\cos \left(\frac{\pi}{3}\right) \sin \left(\frac{\pi}{4}\right)\) Text Transcription: cos(?/3) sin(?/4)

For the following exercises, evaluate the product for the given expression using a sum or difference of two functions. Write the exact answer. \(\2sin \left(\frac{2\pi}{3}\right) \sin \left(\frac{5\pi}{6}\right)\) Text Transcription: 2sin(2?/3) sin(5?/6)

For the following exercises, evaluate the product for the given expression using a sum or difference of two functions. Write the exact answer. \(\2cos \left(\frac{\pi}{5}\right) \cos \left(\frac{\pi}{3}\right)\) Text Transcription: 2cos(?/5) cos(?/3)

For the following exercises, evaluate the sum by using a product formula. Write the exact answer. \(\sin \left(\frac{\pi}{12}\right) - \sin \left(\frac{7\pi}{12}\right)\) Text Transcription: sin (?/12) - sin (7?/12)

For the following exercises, evaluate the sum by using a product formula. Write the exact answer. \(\cos \left(\frac{5\pi}{12}\right) + \cos \left(\frac{7\pi}{12}\right)\) Text Transcription: cos (5?/12) - cos (7?/12)

For the following exercises, find all exact solutions on the interval [0, 2?). \(2 \sin (2 x)+\sqrt{2}=0\) Text Transcription: 2sin(2x) + sqrt 2 = 0

For the following exercises, find all exact solutions on the interval [0, 2?). \(2sin^{2} x ? sin x = 0\) Text Transcription: 2sin^2 x ? sin x = 0

For the following exercises, find all exact solutions on the interval [0, 2?). \(cos^{2} x ? cos x ? 1 = 0\) Text Transcription: cos^2 x ? cos x ? 1 = 0

For the following exercises, find all exact solutions on the interval [0, 2?). \(2sin^{2} x + 5sin x + 3 = 0\) Text Transcription: 2sin^2 x + 5sin x + 3 = 0

For the following exercises, find all exact solutions on the interval [0, 2?). \(\frac{1}{\sec ^{2} x}+2+\sin ^{2} x+4 \cos ^{2} x=0\) Text Transcription: 1 / sec^2 x + 2 sin^2 x + 4cos^2 x = 0

For the following exercises, simplify the equation algebraically as much as possible. Then use a calculator to find the solutions on the interval [0, 2?). Round to four decimal places. \(\sqrt{3} \cot ^{2} x+\cot x=1\) Text Transcription: Sqrt 3 cot^2 x + cot x = 1

For the following exercises, simplify the equation algebraically as much as possible. Then use a calculator to find the solutions on the interval [0, 2?). Round to four decimal places. \(csc^{2} x ? 3csc x ? 4 = 0\) Text Transcription: csc^2 x ? 3csc x ? 4 = 0

For the following exercises, graph each side of the equation to find the zeroes on the interval [0, 2?). \(20cos^{2} x + 21cos x + 1 = 0\) Text Transcription: 20cos^2 x + 21cos x + 1 = 0

For the following exercises, graph each side of the equation to find the zeroes on the interval [0, 2?). \(sec^{2} x ? 2sec x = 15\) Text Transcription: sec^2 x ? 2sec x = 15

For the following exercises, simplify the given expression \(cos(?x)sin x cot x + sin^{2} x\) Text Transcription: cos(?x)sin x cot x + sin^2 x

For the following exercises, simplify the given expression \(csc(?)cot(?)(sec^{2} ? ? 1)\) Text Transcription: csc(?)cot(?)(sec^2 ? ? 1)

For the following exercises, simplify the given expression \(cos^{2} (?) sin^{2} (?) (1 + cot^{2} (?)) (1 + tan^{2} (?))\) Text Transcription: cos^2 (?) sin^2 (?) (1 + cot^2 (?)) (1 + tan^2 (?))

For the following exercises, find the exact value. \(\cos \left(\frac{7 \pi}{12}\right)\) Text Transcription: cos ( 7? / 12)

For the following exercises, find the exact value. \(\tan \left(\frac{3 \pi}{8}\right)\) Text Transcription: tan ( 3? / 8)

For the following exercises, find the exact value. \(\tan \left(\sin ^{-1}\left(\frac{\sqrt{2}}{2}\right)+\tan ^{-1} \sqrt{3}\right)\) Text Transcription: tan (sin^-1 (sqrt 2 / 2) + tan^-1 sqrt 3)

For the following exercises, find the exact value. \(2 \sin \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)\) Text Transcription: 2 sin (?/4) sin (?/6)

For the following exercises, find the exact value. \(\cos \left(\frac{4 \pi}{3}+\theta\right)\) Text Transcription: cos (4?/3 + ?)

For the following exercises, find the exact value. \(\tan \left(-\frac{\pi}{4}+\theta\right)\) Text Transcription: tan (- ? /4 + ?)

For the following exercises, simplify each expression. Do not evaluate. \(cos^{2}(32°)tan^{2}(32°)\) Text Transcription: cos^2(32°)tan^2(32°)

For the following exercises, simplify each expression. Do not evaluate. \(\cot \left(\frac{\theta}{2}\right)\) Text Transcription: cot (?/2)

For the following exercises, find all exact solutions to the equation on [0, 2?). \(cos^{2} x ? sin^{2} x ? 1 = 0\) Text Transcription: cos^2 x ? sin^2 x ? 1 = 0

For the following exercises, find all exact solutions to the equation on [0, 2?). \(cos^{2} x = cos x 4sin^{2} x + 2sin x ? 3 = 0\) Text Transcription: cos^2 x = cos x 4sin^2 x + 2sin x ? 3 = 0

For the following exercises, find all exact solutions to the equation on [0, 2?). \(cos(2x) + sin^{2} x = 0\) Text Transcription: cos(2x) + sin^{2} x = 0

For the following exercises, find all exact solutions to the equation on [0, 2?). \(2sin^{2} x ? sin x = 0\) Text Transcription: 2sin^2 x ? sin x = 0

For the following exercises, find all exact solutions to the equation on [0, 2?). Find all solutions of \(\tan (x)-\sqrt{3}=0\). Text Transcription: tan(x) - sqrt 3 = 0

For the following exercises, find all exact solutions to the equation on [0, 2?). Find the solutions of \(sec^{2} x ? 2sec x = 15\) on the interval [0, 2?) algebraically; then graph both sides of the equation to determine the answer. Text Transcription: sec^2 x ? 2sec x = 15

For the following exercises, find all exact solutions to the equation on [0, 2?). \(2 \cos \left(\frac{\theta}{2}\right)=1\) Text Transcription: 2 cos (?/2) = 1

For the following exercises, find all exact solutions to the equation on [0, 2?). \(\sqrt{3} \cot (y)=1\) Text Transcription: sqrt 3 cot(y) = 1

For the following exercises, find all exact solutions to the equation on [0, 2?). Find sin(2?), cos(2?), and tan(2?) given \(\cot \theta=-\frac{3}{4}\) and ? is on the interval \(\left[\frac{\pi}{2}, \pi\right]\). Text Transcription: cot ? = - 3/4 [?/2, ?]

For the following exercises, find all exact solutions to the equation on [0, 2?). Find sin \(\left(\frac{\theta}{2}\right)\), cos \(\left(\frac{\theta}{2}\right)\), and tan \(\left(\frac{\theta}{2}\right)\) given \(\cos \theta=\frac{7}{25}\) and ? is in quadrant IV. Text Transcription: (?/2) cos ? = 7 / 25

For the following exercises, find all exact solutions to the equation on [0, 2?). Rewrite the expression \(sin^{4} x\) with no powers greater than 1. . Text Transcription: sin^4 x

For the following exercises, prove the identity. \(tan^{3} x ? tan x sec^{2} x = tan(?x)\) Text Transcription: tan^3 x ? tan x sec^2 x = tan(?x)

For the following exercises, prove the identity. \(sin(3x) ? cos x sin(2x) = cos^{2} x sin x ? sin^{3} x\) Text Transcription: sin(3x) ? cos x sin(2x) = cos^2 x sin x ? sin^3 x

For the following exercises, prove the identity. \(\frac{\sin (2 x)}{\sin x}-\frac{\cos (2 x)}{\cos x}=\sec x\) Text Transcription: sin(2x) / sin x - cos(2x) / cos x = sec x

Plot the points and find a function of the form y = Acos(Bx + C) + D that fits the given data.

The displacement h(t) in centimeters of a mass suspended by a spring is modeled by the function \(h(t)=\frac{1}{4} \sin (120 \pi t)\), where t is measured in seconds. Find the amplitude, period, and frequency of this displacement. Text Transcription: h(t) = 1/4 sin(120?t)

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). 2 sin ? = ?1

For the following exercises, find all solutions exactly that exist on the interval [0, 2?). tan x sin x + sin(?x) = 0

For the following exercises, find the exact value. sin(70°)cos(25°) ? cos(70°)sin(25°)

For the following exercises, find the exact value. cos(83°)cos(23°) + sin(83°)sin(23°)

For the following exercises, prove the identity. cot x cos(2x) = ? sin(2x) + cot x

For the following exercises, change the functions from a product to a sum or a sum to a product. sin(9x)cos(3x)

For the following exercises, change the functions from a product to a sum or a sum to a product. cos(7x)cos(12x)

For the following exercises, change the functions from a product to a sum or a sum to a product. sin(11x) + sin(2x)

For the following exercises, change the functions from a product to a sum or a sum to a product. cos(6x) + cos(5x)

For the following exercises, find all exact solutions on the interval [0, 2?). tan x + 1 = 0

For the following exercises, find all exact solutions on the interval [0, 2?). cos x ? 5sin(2x) = 0

For the following exercises, simplify the given expression. sin(?x)cos(?2x)?sin(?x)cos(?2x)

For the following exercises, find all exact solutions to the equation on [0, 2?). Rewrite the sum as a product: cos(2x) + cos(?8x).

For the following exercises, find all exact solutions to the equation on [0, 2?). Rewrite the product as a sum or difference: 8cos(15x)sin(3x)

For the following exercises, find all exact solutions to the equation on [0, 2?). Rewrite the difference as a product: 2sin(8?) ? sin(4?)

A woman is standing 300 feet away from a 2,000- foot building. If she looks to the top of the building, at what angle above horizontal is she looking? A bored worker looks down at her from the 15th floor (1,500 feet above her). At what angle is he looking down at her? Round to the nearest tenth of a degree.

Two frequencies of sound are played on an instrument governed by the equation n(t) = 8cos(20?t)cos(1,000?t). What are the period and frequency of the “fast” and “slow” oscillations? What is the amplitude?

The average monthly snowfall in a small village in the Himalayas is 6 inches, with the low of 1 inch occurring in July. Construct a function that models this behavior. During what period is there more than 10 inches of snowfall?

A spring attached to a ceiling is pulled down 20 cm. After 3 seconds, wherein it completes 6 full periods, the amplitude is only 15 cm. Find the function modeling the position of the spring t seconds after being released. At what time will the spring come to rest? In this case, use 1 cm amplitude as rest.

Water levels near a glacier currently average 9 feet, varying seasonally by 2 inches above and below the average and reaching their highest point in January. Due to global warming, the glacier has begun melting faster than normal. Every year, the water levels rise by a steady 3 inches. Find a function modeling the depth of the water t months from now. If the docks are 2 feet above current water levels, at what point will the water first rise above the docks?