+0  
 
0
738
1
avatar+140 

Given that sinθ=a, with 0<a and that tanθ<0, determine cosθ.

 Jan 16, 2017
 #1
avatar+128090 
0

sinθ=   y/ r = a / 1 = a

 

cosθ =  x / r

 

And

 

1 - sin^2 θ  =  1 - a^2  = cos^2 θ

 

So

 

cos θ  =  ± √ [ 1 - a^2 ]

 

And since  tanθ<0   = sinθ / cosθ = a / cosθ and a > 0.....this angle is in the second quadrant.....so the cosine is negative

 

So

 

cos θ  =   - √ [ 1 - a^2 ]

 

 

 

cool cool cool

 Jan 16, 2017

3 Online Users

avatar