Question #6df80

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Question #6df80

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Answer 1 · 2017-01-16T23:30:19

$sin 2 θ$ $sin2theta$ = $\frac{\sqrt{3}}{2}$ $sqrt3/2$
$cos 2 θ = \frac{1}{2}$ $cos2theta=1/2$

Explanation:

$sin θ = \frac{1}{2}$ $sintheta=1/2$
Draw an equilateral triangle and cut it in half to give a right angle triangle with sides in the ratio 1:2: $\sqrt{3}$ $sqrt3$ ( the hypotenuse is 2 and Pythagoras gives the third side as $\sqrt{3}$ $sqrt3$
From this you can see that the angle whose sign is $\frac{1}{2}$ $1/2$ is $30 d e g r e e s$ $30 degrees$ if $θ = 30$ $theta =30$ then $2 θ = 60 d e g r e e s$ $2theta=60 degrees$
From the same triangle we get sin60 and cos60

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