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Punkte9488
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 #1
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(a)

 

sin2θ+cos2θ=1       by the Pythagorean Identity.

 

(13)2+cos2θ=1        because we are given that  sinθ=13

 

19+cos2θ=1 cos2θ=119 cos2θ=89 cosθ=±89 cosθ=±223

 

Since  θ  is in Quadrant II,  cos θ  must be negative. So   cosθ=223

 

(b)

 

sin(θ+π6)=sinθcosπ6+cosθsinπ6     by the angle sum formula for sin

 

sin(θ+π6)=(13)(32)+(223)(12) sin(θ+π6)=36226 sin(θ+π6)=3226

 

(c)

 

cos(θπ3)=cosθcosπ3+sinθsinπ3     by the angle difference formula for cos

 

Now plug in the values for  cos θ,  cos(pi/3) ,  sin θ , and  sin(pi/3)  and simplify. Can you finish this one?

 

(d)

 

To use the angle sum formula for tan, let's first find  tan θ.

 

tanθ=sinθcosθ=(13)(223)=122=24

 

tan(θ+π4)=tanθ+tanπ41tanθtanπ4     by the angle sum formula for tan

 

tan(θ+π4)=(24)+(1)1(24)(1) tan(θ+π4)=424+2

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10.05.2019