I had this question on my test I took today, and I'm confused if my answer's right.
I had to find the value of
$$\cos^{-1}(\sin(-17))$$
Okay, first, I drew a triangle. And, after, I let a and b for each line related to sin -17, so that we can say sin (-17) is b/a. And then, I realized cos ^(-1)(b/a) is the other angle than -17 and the right angle. I said the answer was 73, subtracting 17 from 90, since I thought -17 was an way of expressing that the triangle is in the third or fourth quadrant, and the actual angle is 17. However, I heard these kids saying that the answer's 107, since the angles should add up to 90, and 107+(-17) =90. I'm simultaneously confused and frustrated. What's the answer?
any help would be appreciated.
Is this what you meant ? $$\cos^{-1}(\sin(-17))=\cos^{-1}(\cos(90-(-17)))=\cos^{-1}(\cos(90+17))= 90+17=107$$
Because you have for complementary angles that
$$\sin(\alpha)=\cos(\frac {\pi}2-\alpha)$$ Or in degree $$\sin(\alpha)=\cos(90-\alpha)$$ but you have $$\alpha =-17$$ So it 's 107