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

2 Answers
Dec 2, 2016

Answer:

#sin"B"=12/13#
#"B"=sin^-1(-12/13)#

Explanation:

Once you have worked out the value of #"B"#, you simply have to type #cos(2"B")# in your calculator to get the answer. However, this will give you the principle value of #2"B"#. To find out the value of #2"B"# in the third quadrant, do #360-cos(2"B")#.

The number of significant figures/decimal places is up to you.
Another tip is that if you want a more accurate answer you can type #cos(2xxsin^-1(-12/13))# into your calculator. This will help you to avoid rounding errors. Then, you can do #360-"ANS"# (instead of rounding).

Dec 3, 2016

Answer:

#cos 2B = -119/169#

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#