91Ó°ÊÓ

Use a sum or difference formula to find the exact value of the given trigonometric function. Do not use a calculator. $$ \sin 75^{\circ} $$

Use the fundamental identities and the even-odd identities to simplify each expression. $$ \frac{\sin \theta}{\csc \theta}+\frac{\cos \theta}{\sec \theta} $$

Find the exact value of the given trigonometric expression. Do not use a calculator. $$ \arccos (-1) $$

Use the techniques of shifting, stretching, compressing, and reflecting to sketch at least one cycle of the graph of the given function. $$ y=2-\sin x $$

Find all solutions of the given trigonometric equation if \(x\) represents an angle measured in radians. $$ \sec x=\sqrt{2} $$

Find the indicated value without the use of a calculator. $$ \cot \frac{13 \pi}{6} $$

In Problems \(1-16\), draw the given angle in standard position. Bear in mind that the lack of a degree symbol \(\left(^{\circ}\right)\) in an angular measurement indicates that the angle is measured in radians. $$ 135^{\circ} $$

Use the techniques of shifting, stretching, compressing, and reflecting to sketch at least one cycle of the graph of the given function. $$ y=3+3 \sin x $$

Use a sum or difference formula to find the exact value of the given trigonometric function. Do not use a calculator. $$ \cos 75^{\circ} $$

Use the fundamental identities and the even-odd identities to simplify each expression. $$ \frac{\csc ^{2} x-1}{\cot x} $$