If cos x = 12/13 and x is an acute angle, how do you find the value of cos (180 - x)?

Question

4285 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-24T20:24:38

#cos(180^@-x)=-12/13#

We will use the cosine angle subtraction formula:

#cos(a-b)=cos(a)cos(b)+sin(a)sin(b)#

Thus:

#cos(180^@-x)=cos(180^@)cos(x)+sin(180^@)sin(x)#

Note that #cos(180^@)=-1# and #sin(180^@)=0#:

#cos(180^@-x)=(-1)cos(x)+(0)sin(x)#

#cos(180^@-x)=-cos(x)#

And since in this scenario #cos(x)=12/13#:

#cos(180^@-x)=-12/13#