SOLUTION: If sin a = 0.2 then cos a must equal?

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Question 323917: If sin a = 0.2 then cos a must equal?
Answer by Edwin McCravy(20086) About Me  (Show Source):
You can put this solution on YOUR website!

If sin a = 0.2 then cos a must equal?

Since sine%22%22=%22%22%28opposite%29%2F%28hypotenuse%29 and since

0.2%22%22=%22%22 the fraction 0.2%2F1 if we draw a right triangle
with one side equal to the numerator 0.2 of that fraction and the
hypotenuse equal to the denominator of that fraction 1, then the
angle that the side that equals 0.2 is opposite to will be angle a:


 
Since cosine%22%22=%22%22%28adjacent%29%2F%28hypotenuse%29 all we need
do is calculate the side adjacenet to angle a, which is the bottom side,
call it x.



We use the Pythagorean theorem to calculate x:

adjacent%5E2%2Bopposite%5E2=hypotenuse%5E2
x%5E2%2B%280.2%29%5E2=1%5E2
x%5E2%2B0.04=1
x%5E2=.96
x%5E2=96%2F100
x%5E2=24%2F25
x=sqrt%2824%2F25%29
x=sqrt%2824%29%2Fsqrt%2825%29
x=sqrt%2824%29%2F5
x=sqrt%284%2A6%29%2F5
x=2sqrt%286%29%2F5

So cos%28a%29%22%22=%22%22adjacent%2F%28hypotenuse%29%22=%22%282sqrt%286%29%2F5%29%2F1%22%22=%22%222sqrt%286%29%2F5

The decimal value of that is 0.9797958971, and you can get that
just by using your TI-84 calculator

cos(sin-1(0.2))
     .9797958971  

Edwin