How do you simplify # cos (pi - theta)#?

2 Answers
Aug 18, 2016

-cos t

Explanation:

Trig unit circle gives:
cos (pi - t) = -cos t

Aug 18, 2016

#cos(pi-theta)=-cos(theta)#

Explanation:

While a different answer mentions the unit circle, another way of arriving at the solution is to use the identity
#cos(alpha+beta) = cos(alpha)cos(beta)-sin(alpha)sin(beta)#
along with the fact that #cos(-alpha) = cos(alpha)#

With that, we have

#cos(pi-theta) = cos(pi+(-theta))#

#=cos(pi)cos(-theta)-sin(pi)sin(-theta)#

#=(-1)cos(-theta) - 0sin(-theta)#

#=-cos(-theta) - 0#

#=-cos(-theta)#

#=-cos(theta)#