For the first part we will use that cosθ=x2+y2x,sinθ=x2+y2y :
- cosθ=32+423=53=0.6 , sinθ=54=0.8
- cosθ=22+22−2=22−2=−21, sinθ=222=21
For the second part we will use that cos2θ+sin2θ=1 and quadrant to determine the sign :
- cos2θ+41=1,cos2θ=43, in Q1 cosθ≥0, so cosθ=23
- 3625+sin2θ=1,sin2θ=3611, Q11 (which is the same as Q3, as every 4 quadrants we do a full turn) sinθ≤0, so sinθ=−611
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