Question

if the angles X and Y each measure between 90° and 180°, and if sinX = -cosY, what is the sum of the measures of the angles X and Y?

Answer 1

We have the following:

We have that the cosine and the sine are equal their quotient, that is, tangent, is 1. And this happens when the angle is 45 degrees.

`\begin{gathered} \sin X=-\cos Y \\ \tan (X)/(Y)=1 \end{gathered}`

We know that the second quadrant (between 90 and 180 degrees), the sine is negative and the cosine is positive, therefore, in 135 (90 + 45) degree it will be -1.

Therefore the answer is:

`\begin{gathered} X=135 \\ Y=135 \\ X+Y=135+135=270 \end{gathered}`