SOLUTION: given that cos2a =2/5 and 0<2a<90, determine the exact values of sin a, cos a, tan a, csc a, sec a, and cot a.

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Question 887545: given that cos2a =2/5 and 0<2a<90, determine the exact values of sin a, cos a, tan a, csc a, sec a, and cot a.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
Since a is in the first quadrant, everything will be positive, so
when we take square roots we only need to take positive square
roots.



Use the identity 





, that's the cosine.
You can rationalize the denominator if you like.

Then use the identity 



Use the identity: 



, that's the sine.

Then use the identity 

, that's the cosecant.

Use the identity  
  

, that's the tangent

Use the identity  
  
, that's the cotangent.

So that's all six.

Edwin


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