How do you use a double angle identity to find the exact value of each expression?

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How do you use a double angle identity to find the exact value of each expression?

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Answer 1 · 2015-03-06T15:06:28

You would need an expression to work with.

For example:
Given $sin α = \frac{3}{5}$ $sinalpha=3/5$ and $cos α = - \frac{4}{5}$ $cosalpha=-4/5$ , you could find $sin 2 α$ $sin2 alpha$ by using the double angle identity
$sin 2 α = 2 sin α cos α$ $sin2 alpha=2sin alpha cos alpha$ .

$sin 2 α = 2 (\frac{3}{5}) (- \frac{4}{5}) = - \frac{24}{25}$ $sin2 alpha=2(3/5)(-4/5)=-24/25$ .

You could find $cos 2 α$ $cos2 alpha$ by using any of:
$cos 2 α = {cos}^{2} α - {sin}^{2} α$ $cos2 alpha=cos^2 alpha -sin^2 alpha$
$cos 2 α = 1 - 2 {sin}^{2} α$ $cos2 alpha=1 -2sin^2 alpha$
$cos 2 α = 2 {cos}^{2} α - 1$ $cos2 alpha=2cos^2 alpha -1$

In any case, you get $cos α = \frac{7}{25}$ $cos alpha=7/25$ .

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How do you use a double angle identity to find the exact value of each expression?

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