How do you evaluate cos−1(√32) without a calculator?

1 Answer
Annie
Aug 31, 2016

30 degrees or 16π

Explanation:

If you draw an equilateral triangle and cut it in half the ratio of the hypotenuse and the shorter other side are 2:1 Pythagoras gives us the third side as √3

From this triangle tan 60 =√3, cos 60 =12, sin 60=√32
And in the same what you have the exact values for sin , cos and tan of 30.

The other triangle which is useful is the isosceles right angle triangle whic gives exact ratios for sin cos and tan of 45 degrees

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