SOLUTION: I have two questions :). 1. Use a calculator to find the approximate value of cos^-1(0.78). 2. Find the exact value of tan (arcsin (two fifths)). Please explain your reasoning.

Algebra ->  Rational-functions -> SOLUTION: I have two questions :). 1. Use a calculator to find the approximate value of cos^-1(0.78). 2. Find the exact value of tan (arcsin (two fifths)). Please explain your reasoning.       Log On


   

Question 1015673: I have two questions :).
1. Use a calculator to find the approximate value of cos^-1(0.78).
2. Find the exact value of tan (arcsin (two fifths)). Please explain your reasoning.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
In your calculator, press .78.
Hit arc cos button.
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.
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sin%28theta%29=2%2F5
So then,
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1
%282%2F5%29%5E2%2Bcos%5E2%28theta%29=1
4%2F25%2Bcos%5E2%28theta%29=1
cos%5E2%28theta%29=21%2F25
cos%28theta%29=0+%2B-+sqrt%2821%29%2F5
So then,
tan%28theta%29=%282%2F5%29%2F%280+%2B-+sqrt%2821%29%2F5%29
tan%28theta%29=0+%2B-+2%2Fsqrt%2821%29
tan%28theta%29=0+%2B-+%282%2F21%29sqrt%2821%29