SOLUTION: Find the exact value of tan [arcsin (2/5)]. For full credit, explain your reasoning.

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Question 1086583: Find the exact value of tan [arcsin (2/5)]. For full credit, explain your reasoning.

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
You have an angle alpha such that sin%28alpha%29 = 2%2F5.


In addition, you know that alpha is in QI.


Hence, cosalpha%29 = sqrt%281-sin%5E2%28alpha%29%29 = sqrt%281-%282%2F5%29%5E2%29 = sqrt%28%2825-4%29%2F25%29 = sqrt%2821%29%2F5.


Then tan%28alpha%29 = sin%28alpha%29%2Fcos%28alpha%29 = %28%282%2F5%29%29%2F%28%28sqrt%2821%29%2F5%29%29 = 2%2Fsqrt%2821%29 = %282%2Asqrt%2821%29%29%2F21.

Solved.