How do you find the exact values of the six trigonometric function of $theta$ if the terminal side of $theta$ in the standard position contains the point (-1,0)?

Question

3517 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-08-01T12:28:44

Please see below.

Given that ,terminal side of $theta$ in the standard position contains the point $(-1,0)$

Let us use the unit circle.

enter image source here

So, $theta=pi,3pi,5pi,...etc.$

$:.sintheta=sinpi=sin3pi=...=0$

$andcostheta=cospi=cos3pi=...=-1$

Hence,

$(1)sintheta=0$

$(2)costheta=-1$

$(3)tantheta=(sintheta)/(costheta)=0/(-1)=0$

$(4)csctheta=1/sintheta=1/0to "undefined"$

$(5)sectheta=1/costheta=1/(-1)=-1$

$(6)cottheta=1/tantheta=1/0to "undefined"$

How do you find the exact values of the six trigonometric function of thetatheta if the terminal side of thetatheta in the standard position contains the point (-1,0)?