if cos 45=1/sqrt2, find cos 315, sin 270, sin 210, tan 210

sibuzwaW

sibuzwaW

Answered question

2021-01-25

if cos⁡45=12, find cos⁡315,sin⁡270,sin⁡210,tan⁡210

Answer & Explanation

komunidadO

komunidadO

Skilled2021-01-26Added 86 answers

cos⁡45=12,sin⁡45=1−cos2(45)=1−12=12=12=cos⁡45,
sin⁡90=sin⁡(2⋅45)=2sin⁡45cos⁡45=2⋅12⋅12=1,cos⁡90=cos⁡(2⋅45)=cos⁡45cos⁡45−sin⁡45sin⁡45=12−12=0,
sin⁡180=sin⁡(2⋅90)=2sin⁡90cos⁡90=0,cos⁡180=cos⁡(2⋅90)=cos⁡90cos⁡90−sin⁡90sin⁡90=0−1=−1,
cos⁡(X)=cos⁡(−X),so cos⁡45=cos⁡(−45)=cos⁡(360−45)=cos⁡(315)=12.
sin⁡270=sin⁡(180+90)=sin⁡180cos⁡90+cos⁡180sin⁡90=0−1=−1.
sin⁡3X=sin⁡(2X+X)=sin⁡2Xcos⁡X+cos⁡2Xsin⁡X=2sin⁡Xcos2(X)+cos2(X)sin⁡(X)−sin3(X),soif3X=90:
1=2sin⁡30(1−sin2(30))+(1−sin2(30))sin⁡(30)−sin3(30

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