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:

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

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