# Using cast diagram to solve equation

I have the question

Solve each equation for $X$ in the interval $0\leq X\leq 360$

$$\sin(X-30) = -0.3$$

Here is my attempt:

$\sin$ is negative and so $\tan$ and $\cos$ are positive.

This would mean that $17.5$ is added to $180$ and subtracted from $360$.

So the final answers for $X$ should be $227.5$ and $372.5$ degrees.

However, the solutions say that $X$ should be $12.5$ and $227.5$.

Why isn't the $360$ degrees from the cast diagram used? From previous questions it is but for this question it isn't?

Is there a mistake or is there a specific rule for this question and if so what is it ?

• are the angles in degrees? – Dr. Sonnhard Graubner Mar 16 '17 at 15:18
• Yes they are :) – Dan Mar 16 '17 at 15:19
• Be careful. $372.5^\circ > 360^\circ$, so you must find an angle coterminal with $372.5^\circ$ between $0^\circ$ and $360^\circ$. – N. F. Taussig Mar 16 '17 at 15:27