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Given sin(−θ)=−14 and tanθ=15√15

SamJones  Feb 21, 2018
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sin( -θ )    =   - sin θ  
- 1/4 =

- sin θ

 

 

1/4 = sin θ  

 

sin2θ  +  cos2θ   =   1

 

(1/4)2  +  cos2θ   =   1

 

cos2θ   =   1  -  (1/4)2

 

cos2θ   =   1  -  1/16

 

cos2θ   =   15/16

 

cos θ   =   ±√[ 15/16 ]

 

cos θ   =   ±√15 / 4

 

Since  sin θ  is positive and  tan θ  is positive,  cos θ must be positive.

 

cos θ   =   √15 / 4

hectictar  Feb 21, 2018

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