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## 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?

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