삼각함수

For the following exercises, find a. the amplitude, b. the period, and c. the phase shift with direction for each function.

$y=-3\sin (\pi x+2)$

For the following exercises, find a. the amplitude, b. the period, and c. the phase shift with direction for each function.

$y=4\cos \left(2x-\frac{\pi }{2}\right)$

[T] Find the length of the arc intercepted by central angle $\theta$ in a circle of radius r. Round to the nearest hundredth.

a. $r=12.8$ cm, $\theta =\frac{5\pi }{6}$ rad b. $r=4.378$ cm, $\theta =\frac{7\pi }{6}$ rad c. $r=0.964$ cm, $\theta =50^\circ$ d. $r=8.55$ cm, $\theta =325^\circ$

[T] A total of 250,000 m² of land is needed to build a nuclear power plant. Suppose it is decided that the area on which the power plant is to be built should be circular.

a. Find the radius of the circular land area. b. If the land area is to form a $45^\circ$ sector of a circle instead of a whole circle, find the length of the curved side.