How do you evaluate sine, cosine, tangent of #-150^circ# without using a calculator?

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Answer 1 · 2017-01-29T10:11:01

See explanation.

First let's calculate #sin(-150)#

#sin(-150)=-sin150#

we can write this, because #sinx# is an odd function.

#-sin150=-sin(180-30)=-sin30=-1/2#

Now we can calculate #cos(-150)# using:

#sin^2x+cos^2x=1#

#(-1/2)^2+cos^2(-150)=1#

#cos^2(-150)=1-1/4#

#cos^2(-150)=3/4#

#cos(-150)=-sqrt(3)/2#

We choose the negative value because the end arm of the angle lies in the third quadrant, and in this quadrant #sin# and #cos# are negative.

Tio calculate #tan(-150)# using:

Here it is:

#tan(-150)=sin(-150)/cos(-150)=-1/2-:(-sqrt(3)/2)=#

#=1/2xx2/sqrt(3)=1/sqrt(3)=sqrt(3)/3#