# Trig Identities

Mike_Winegar

## Homework Statement

Problem 6. If you know that tan(theta) = -4/5 and sin(theta) > 0, find:
(a) sin(theta)
(b) cos(theta)
(c) tan(theta + pi)

## Homework Equations

cos^2(t)+sin^2(t)=1
tan(t)=sin(t)/cos(t)

## The Attempt at a Solution

My teacher went over this today, but likes to skip over steps that I just don't understand. What I've done so far...

-4/5=sin(t)/cos(t)

sin(t)=(-4cos(t)/5)
solved for sin(t)

((-4cos(t)/5)/cos(t))
plugged sin(t) equation back into original equation

ends up being
(-4cos^2(t)/5)=-4/5

We then have the identity that cos^2 + sin^2 = 1

Here's where I get lost. My teacher jumped it directly to:
(-4/5 cos(t))^2 +cos^2(t)=1

I assume you would plug in our original sin(t)=(-4cos(t)/5) into the above identity, but I have no clue as to how she did that without having an additional 4/5th where she substituted the cos side of the equation in for the sin portion of the identity.

Any help would be appreciated.

Lollol

I think I just figured it out actually. Was my teacher using the Pythagorean theorem and not a trig identity?
So:
(-4/5 cos)^2 + cos^2 =r^2
(-4/5 cos)^2 + cos^2 =1?

Last edited:

## Answers and Replies

TylerH
To do these, it will help if you recall the geometric definitions of the trig functions. tan is opposite over adjacent. So, think of an angle in a triangle, with opposite=-4 and adjacent=5. Find the hypotenuse, then use SOH-CAH-TOA.