# If #sin B = -12/13# then what is #cos 2B# ?

##### 2 Answers

#### Explanation:

Once you have worked out the value of

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#### Explanation:

Given:

#sin B = -12/13#

Then:

#cos 2B = 2 cos^2 B - 1#

#color(white)(cos 2B) = 2(1-sin^2 B) - 1#

#color(white)(cos 2B) = 1-2 sin^2 B#

#color(white)(cos 2B) = 1-2 (-12/13)^2#

#color(white)(cos 2B) = 1-288/169#

#color(white)(cos 2B) = (169-288)/169#

#color(white)(cos 2B) = -119/169#