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Expert: - 4/12/2011


Question
What is sin of the arc-cos of -3/5?

how would you solve this without a calculator

Answer
Hi Faiqa,
A couple of ways but i think its easiest if you apply the identity;
cos²x + sin²x = 1
sin²x = 1 - cos²x
sinx = √(1 - cos²x)
So, if arccos(-3/5) = x
cosx = -3/5
sinx = √(1 - (-3/5)²)
= √(1 - 9/25)
= √(16/25)
= ±4/5
The sign you choose would depend on the quadrant in which the angle x lies.

Regards

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