Here are my trigonmetric ratios, for a point Q(-3, 6) that's on the terminal arm of an angle θ:
\(tan θ = {-2}\), \(sinθ = {2 \sqrt{5} \over 5}\), \(cosθ = -{ \sqrt{5} \over 5}\)
To find θ, I just plugged in inverse than input my values into my calculator (which was in degree mode). For tangent and sine, I got 63.4° (which is the reference angle to the actual angle we're looking for). However, for cosine I got 116.6°, which is not the reference angle (and from what I know, don't you get the reference angle from inputting these values?). I just wanna know how is this possible? Why am I getting different answers is really confusing me...
+33615 (-3, 6) means the arm is in the second quadrant. Notice that 63.4 + 116.6 = 180. Your calculator is giving you the angle between the arm and the negative x-axis for tan-1 and sin-1 ; and is giving you the angle between the arm and the positive x-axis in the case of cos-1.
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