Chapter 6

State the amplitude, period, and phase shift of the function. \(g(t)=3 \sin (2 t-\pi)\)

Find the rule of the product function fg. $$f(t)=3 \sin t ; \quad g(t)=\sin t+2 \cos t$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\sin (3 \pi / 2)$$

Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 9\) of a circle

In Exercises \(1-6,\) determine the quadrant containing the termi. nal side of an angle of t radians in standard position under the given conditions. $$\cos t>0 \quad \text { and } \quad \sin t<0$$

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\sin t=0$$

State the amplitude, period, and phase shift of the function. \(h(t)=-6 \cos (4 t-\pi / 4)\)

Find the rule of the product function fg. $$f(t)=5 \tan t ; \quad g(t)=\tan ^{3} t-1$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\sin (-\pi)$$

Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 24\) of a circle

In Exercises \(1-6,\) determine the quadrant containing the termi. nal side of an angle of t radians in standard position under the given conditions. $$\begin{aligned} &\sin t<0 \quad \text { and }\\\ &\tan t>0 \end{aligned}$$

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\cos t=0$$

State the amplitude, period, and phase shift of the function. \(q(t)=-5 \sin (5 t+1 / 5)\)

Find the rule of the product function fg. $$f(t)=3 \sin ^{2} t ; \quad g(t)=\sin t+\tan t$$

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\sin t=1$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\cos (3 \pi / 2)$$

Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 18\) of a circle

In Exercises \(1-6,\) determine the quadrant containing the termi. nal side of an angle of t radians in standard position under the given conditions. $$\sec t<0 \quad \text { and } \quad \cot t<0$$

State the amplitude, period, and phase shift of the function. \(g(t)=97 \cos (14 t+5)\)

Find the rule of the product function fg. $$f(t)=\sin 2 t+\cos ^{4} t ; \quad g(t)=\cos 2 t+\cos ^{2} t$$

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\sin t=-1$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\cos (-\pi / 2)$$

Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 72\) of a circle

In Exercises \(1-6,\) determine the quadrant containing the termi. nal side of an angle of t radians in standard position under the given conditions. $$\begin{aligned} &\csc t<0 \quad \text { and }\\\ &\sec t>0 \end{aligned}$$

State the amplitude, period, and phase shift of the function. \(f(t)=\cos 2 \pi t\)

Factor the given expression. $$\cos ^{2} t-4$$

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\cos t=-1$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\tan (4 \pi)$$

Find the radian measure of the angle in standard position formed by rotating the terminal side by the given amount. \(1 / 36\) of a circle

In Exercises \(1-6,\) determine the quadrant containing the termi. nal side of an angle of t radians in standard position under the given conditions. $$\sec t>0 \quad \text { and } \quad \cot t<0$$

State the amplitude, period, and phase shift of the function. \(k(t)=\cos (2 \pi t / 3)\)

Use the graphs of the sine and cosine functions to find all the solutions of the equation. $$\cos t=1$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\tan (-\pi)$$

State the amplitude, period, and phase shift of the function. \(p(t)=6 \cos (3 \pi t+1)\)

In Exercises \(7-16,\) evaluate all six trigonometric finctions at \(t\) where the given point lies on the reminal side of an angle of \(t\) radians in standard position. $$(3,4)$$

Factor the given expression. $$\sin ^{2} t-\cos ^{2} t$$

Find tan \(t,\) where the terminal side of an angle of t radians lies on the given line. $$y=11 x$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\cos (-3 \pi / 2)$$

(a) What is the period of \(f(t)=\sin 2 \pi t ?\) (b) For what values of \(t\) (with \(0 \leq t \leq 2 \pi\) ) is \(f(t)=0 ?\) (c) For what values of \(t\) (with \(0 \leq t \leq 2 \pi\) ) is \(f(t)=1 ?\) or \(f(t)=-1 ?\)

In Exercises \(7-16,\) evaluate all six trigonometric finctions at \(t\) where the given point lies on the terminal side of an angle of \(t\) radians in standard position. $$(0,6)$$

Factor the given expression. $$\sin ^{3} t-\sin t$$

Find tan \(t,\) where the terminal side of an angle of t radians lies on the given line. $$y=1.5 x$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\sin (9 \pi / 2)$$

Give the rule of a periodic function with the given numbers as amplitude, period, and phase shift (in this order) $$3, \pi / 4, \pi / 5$$

In Exercises \(7-16,\) evaluate all six trigonometric finctions at \(t\) where the given point lies on the terminal side of an angle of \(t\) radians in standard position. $$(-5,12)$$

Factor the given expression. $$\tan ^{2} t+6 \tan t+9$$

Find tan \(t,\) where the terminal side of an angle of t radians lies on the given line. $$y=1.4 x$$

In Exercises \(1-10,\) use the definition (not a calculator) to find the function value. $$\cos (-11 \pi / 2)$$

Give the rule of a periodic function with the given numbers as amplitude, period, and phase shift (in this order) $$4,5,0$$

In Exercises \(7-16,\) evaluate all six trigonometric finctions at \(t\) where the given point lies on the terminal side of an angle of \(t\) radians in standard position. $$(-2,-3)$$