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# Wondering on how the value of θ is determined?

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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...

Aug 6, 2018
edited by Guest  Aug 6, 2018
edited by Guest  Aug 6, 2018