Problem 6. If you know that tan(theta) = -4/5 and sin(theta) > 0, find:
(c) tan(theta + pi)
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...
solved for sin(t)
plugged sin(t) equation back into original equation
ends up being
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.
I think I just figured it out actually. Was my teacher using the Pythagorean theorem and not a trig identity?
(-4/5 cos)^2 + cos^2 =r^2
(-4/5 cos)^2 + cos^2 =1?