How do you find $cos60$ using the fundamental identities if you given $sin30=1/2$ ?

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Answer 1 · 2015-02-05T20:00:25

I would use the double angle formula:
$cos(2theta)=cos^2(theta)-sin^2(theta)$

and the fact that:
$sin^2(theta)+cos^2(theta)=1$
giving: $cos^2(theta)=1-sin^2(theta)$

So you get:
$cos(2theta)=cos^2(theta)-sin^2(theta)=$
$=1-sin^2(theta)-sin^2(theta)$ substituting for:

for $theta =30°$ and
$sin(30°)=1/2$
You get:
$cos(60°)=1-1/4-1/4=1/2$

How do you find cos60cos60 using the fundamental identities if you given sin30=1/2sin30=1/2?