Chapter 6

List the transformations needed to change the graph of \(f(t)\) into the graph of \(g(t) .\) ISee Section 3.4 .1 $$f(t)=\sin t ; \quad g(t)=\sin (t-2)$$

In Exercises \(21-25,\) evaluate all six trigonometric finctions at the given number without using a calculator. $$\frac{4 \pi}{3}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$5 \pi / 6$$

Find the radian measure of an angle in standard position that has measure between 0 and \(2 \pi\) and is coterminal with the angle in standard position whose measure is given. $$19 \pi / 4$$

List the transformations needed to change the graph of \(f(t)\) into the graph of \(g(t) .\) ISee Section 3.4 .1 $$f(t)=\cos t ; \quad g(t)=3 \cos (t+2)-3$$

In Exercises \(21-25,\) evaluate all six trigonometric finctions at the given number without using a calculator. $$-\frac{7 \pi}{6}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$3 \pi$$

Find the radian measure of an angle in standard position that has measure between 0 and \(2 \pi\) and is coterminal with the angle in standard position whose measure is given. $$16 \pi / 3$$

In Exercises \(21-25,\) evaluate all six trigonometric finctions at the given number without using a calculator. $$\frac{7 \pi}{4}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-23 \pi / 6$$

Find the radian measure of an angle in standard position that has measure between 0 and \(2 \pi\) and is coterminal with the angle in standard position whose measure is given. $$-7 \pi / 5$$

In Exercises \(21-25,\) evaluate all six trigonometric finctions at the given number without using a calculator. $$\frac{11 \pi}{3}$$

Determine if it is possible for a number to satisfy the given conditions. [Hint: Think Pythagorean.] $$\cos t=8 / 17 \text { and } \tan t=15 / 8$$

Find the radian measure of an angle in standard position that has measure between 0 and \(2 \pi\) and is coterminal with the angle in standard position whose measure is given. $$45 \pi / 8$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$11 \pi / 6$$

(a) State the rule of a function of the form $$f(t)=A \sin (b t+c)$$ whose graph appears to be identical with the given graph. (b) State the rule of a function of the form $$g(t)=A \cos (b t+c)$$ whose graph appears to be identical with the given graph. (Check your book to see graph)

Use the Pythagorean identity to find sin \(t\). $$\cos t=-.5 \quad \text { and } \quad \pi

In Exercises \(21-25,\) evaluate all six trigonometric finctions at the given number without using a calculator. $$ \frac{-11 \pi}{4} $$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-19 \pi / 3$$

Use the Pythagorean identity to find sin \(t\). $$\cos t=-3 / \sqrt{10} \quad \text { and } \quad \pi / 2

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-10 \pi / 3$$

Sketch a complete graph of the function. $$k(t)=-3 \sin t$$

Use the Pythagorean identity to find sin \(t\). $$\cos t=1 / 2 \quad \text { and } \quad 0

Convert the given degree measure to radians. $$6^{\circ}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-15 \pi / 4$$

Sketch a complete graph of the function. $$y(t)=-2 \cos 3 t$$

Use the Pythagorean identity to find sin \(t\). $$\cos t=2 / \sqrt{5} \quad \text { and } \quad 3 \pi / 2

Convert the given degree measure to radians. $$-12^{\circ}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-25 \pi / 4$$

Sketch a complete graph of the function. $$p(t)=-\frac{1}{2} \sin 2 t$$

(a) Find the average rate of change of \(f(t)=\tan t\) from \(t=2\) to \(t=2+h,\) for each of these values of \(h: 01\) \(.001, .0001,\) and .00001 (b) Compare your answers in part (a) with the number (sec \(2)^{2}\). What would you guess that the instantaneous rate of change of \(f(t)=\tan t\) is at \(t=2 ?\)

Convert the given degree measure to radians. $$-12^{\circ}$$

In Exercises \(15-29,\) find the exact value of the sine, cosine, and tangent of the number, without using a calculator. $$-17 \pi / 2$$

Sketch a complete graph of the function. $$q(t)=\frac{2}{3} \cos \frac{3}{2} t$$

Assume that \(\sin t=3 / 5\) and \(0< t <\pi / 2 .\) Use identities in the text to find the number. $$\sin (t+10 \pi)$$

Convert the given degree measure to radians. $$36^{\circ}$$

Sketch a complete graph of the function. $$h(t)=3 \sin (2 t+\pi / 2)$$

Use the graphs of the trigonometric functions to determine the number of solutions of the equation between 0 and \(2 \pi\) \(\sin t=3 / 5[\)Hint: How many points on the graph of \(f(t)=\sin t\) between \(t=0\) and \(t=2 \pi\) have second coordinate \(3 / 5 ?]\)

In Exercises \(30-36,\) perform the indicated operations, then simplify your answers by using appropriate definitions and identities. $$\cos t \sin t(\csc t+\sec t)$$

In Exercises \(31-36\), write the expression as a single real mum. ber. Do not use decimal approximations. IHint: Exercises \(15-21 \text { may be helpful. }]\) $$\sin (\pi / 3) \cos (\pi)+\sin (\pi) \cos (\pi / 3)$$

Convert the given degree measure to radians. $$75^{\circ}$$

Sketch a complete graph of the function. $$p(t)=3 \cos (3 t-\pi)$$

Use the graphs of the trigonometric functions to determine the number of solutions of the equation between 0 and \(2 \pi\) $$\cos t=-1 / 4$$

In Exercises \(30-36,\) perform the indicated operations, then simplify your answers by using appropriate definitions and identities. $$(1+\cot t)^{2}$$

Convert the given degree measure to radians. $$-105^{\circ}$$

In Exercises \(31-36\), write the expression as a single real mum. ber. Do not use decimal approximations. IHint: Exercises \(15-21 \text { may be helpful. }]\) $$\sin (\pi / 6) \cos (\pi / 2)-\cos (\pi / 6) \sin (\pi / 2)$$

Graph the function over the interval \([0,2 \pi)\) and determine the location of all local maxima and minima. [This can be done either graphically or algebraically.] $$f(t)=\frac{1}{2} \sin \left(t-\frac{\pi}{3}\right)$$

Use the graphs of the trigonometric functions to determine the number of solutions of the equation between 0 and \(2 \pi\) $$\tan t=4$$

Assume that \(\sin t=3 / 5\) and \(0< t <\pi / 2 .\) Use identities in the text to find the number. $$\tan t$$

In Exercises \(30-36,\) perform the indicated operations, then simplify your answers by using appropriate definitions and identities. $$(1-\sec t)^{2}$$