Question

Solve the equation sin theta = 0.3 to the nearest tenth. Use the restrictions 90degrees < theta < 180degrees.

A)
θ=107.5


B)
θ=162.5


C)
θ=197.5


D)
θ=17.5

Answer 1

take the arcsine of both sides

remember to subtract that result from 180 because you're in quadrant II

Answer 2

How do you find the arcsine of both sides?

Answer 3

the arcsine of sin(theta) is just theta

so you're left with theta on the left side

Answer 4

the arcsine of 0.3 is

arcsin(3) = 17.4576

use a calculator to find this

Answer 5

oops meant to write

arcsin(0.3) = 17.4576

Answer 6

subtract this result from 180 to get your answer

Answer 7

I got 162.5424
So its B?

Answer 8

There are two easy ways to solve this problem. The first is simple elimination. If theta is bounded between 90 and 180 degrees, clearly neither C nor D can be the right answer. This just leaves us with A and B - if we calculate sin(107.5) = 0.95 and sin(162.5) = 0.3, we see that B is the right answer.

However, the purpose of this question is probably to test your understanding of inverse trigonometric functions. Sin^(-1), or arcsin, of a value given by sin(x) returns x; ie, arcsin(sin(x)) = x.
arcsin(0.3) = 17.5, answer D. But 17.5 is not in the 90-180 range, so this is not the correct answer. If we look at the other 3 answers, A is 90 + 17.5, B is 180 - 17.5, and C is 180 + 17.5. In the case of inverse sine, sin(x) = sin(180 - x), so B is the right answer.

Answer 9

you are correct, B is your answer