What are the exact values of cos 150° and sin 150°?

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Nov 30, 2016

Answer:

#cos(150) = - sqrt3 /2#

#sin(150)= 1/2#

Explanation:

To find cos(150) use the cosine addition formula to add 60 degrees and 90 degrees.

#cos(a+b)=cosacosbcolor(red)-sinasinb#

#cos(90+60)=cos90cos60-sin90sin60#

#cos(90+60)= 0*1/2-1*sqrt3 /2#

#cos(150) = - sqrt3 /2#

For sin(150) use the sine addition formula

#sin(a+b)= sinacosb +cosasinb#

#sin(90+60)=sin90cos60 + cos90sin60#

#sin(90+60)=1*1/2+0*sqrt3 /2#

#sin(150) = + 1/2#

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Using the common angles above you can add or subtract them to determine the sine and cosine of other angles.

As an example, to determine cos(75) you could use the cosine addition formula to add 45 and 30 degrees.

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