Question

Question #76db0

Answer 1

`theta = 0.2662pi and 0.7338pi` are the solutions in the interval [0, 2(pi)].

Explanation:

The steps used on my calculator: Go to RAD mode. Enter `sin^-1(0.7422)`. Result was 0.8363.

Then I divided by `pi:" "0.8363/pi = 0.2662`
Therefore `0.8363 = 0.2662pi`.

Since the interval was given in terms of `pi`, it seems likely that the answer should be in terms of `pi`.

Therefore the 1st solution is `0.2662pi`.

Visualize a sine wave in the interval `0 to 2pi` and find the point `theta = 0.2662pi` (that would be about 48 degrees).

Recognize that the wave is at the same displacement from zero a 2nd time, about 1/2 way past the peak. (About `48^@` to the left of `180^@`.)

So the 2nd solution would be when theta equals
`pi - 0.2662pi = 0.7338pi`

I hope this helps,
Steve