91Ó°ÊÓ

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

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

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

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

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

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

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 \(2 \pi\) $$\tan t=4$$