91Ó°ÊÓ

The terminal side of the angle \(\beta\) in standard position passes through the point (-3,6) . Find exact values for \(\sin (\beta), \cos (\beta),\) and \(\tan (\beta)\).

Two angles of a triangle are \(32^{\circ} 37^{\prime}\) and \(48^{\circ} 39^{\prime} .\) Find the third angle in degrees-minutes-seconds format.

If \(\alpha\) is an angle in standard position whose terminal side intersects the unit circle at the point \((x, y),\) then \(\sin (\alpha)=\) __________ and \(\cos (\alpha)=\)__________.

The graph of \(y=3 \cos (5(x-\pi))+7\) is a _________ wave.

Determine the amplitude, phase shift, and range for each function. Sketch at least one cycle of the graph and label the five key points on one cycle as done in the examples. $$ f(x)=\cos (x)+2 $$

Evaluate each trigonometric function if possible. a. \(\sin (7 \pi / 6)\) b. \(\cos (3 \pi)\) c. \(\tan (-3 \pi / 4)\) d. \(\sec (\pi / 2)\) e. \(\csc (\pi / 3)\) f. \(\cot (-\pi / 4)\)

Determine the amplitude, phase shift, and range for each function. Sketch at least one cycle of the graph and label the five key points on one cycle as done in the examples. $$ y=-\sin (x)+2 $$

Find the equation of each sine wave in its final position. The graph of \(y=\sin (x)\) is shifted \(\pi / 7\) units to the left and reflected in the \(x\) -axis.

Find the equation of each sine wave in its final position. The graph of \(y=\sin (x)\) is reflected in the \(x\) -axis, shrunk by a factor of \(\frac{1}{2},\) shifted \(\pi / 3\) units to the right, and then translated upward 4 units.