Question

Find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of -1.

Answer 1

so how would I evaluate to find the y value?

Answer 2

so you have the angle, and you have the x-coordinate
so you just need the y-coordinate

so, we need a trig identity that uses both "x" and "y" so we can find "y" by solving for "y" :)

do you see any there -> http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png ?

Answer 3

the tangent which is opp/adj which would be y/x which would be y/-1...right? and then what do I need to do?

Answer 4

\(\bf tan(\theta) = \cfrac{opposite}{adjacent} \implies \cfrac{b}{a} \implies \cfrac{y}{x} \\
tan\left(\frac{3\pi}{4}\right) = \cfrac{y}{x} \implies \cfrac{y}{-1}\quad \\\quad \\
tan\left(\frac{3\pi}{4}\right) = \cfrac{y}{-1} \implies -1\times tan\left(\frac{3\pi}{4}\right) = y\)

Answer 5

woops... negative angle rather... lemme rewrite that

Answer 6

ok take your time I really appreciate the help!!!

Answer 7

\(\bf tan(\theta) = \cfrac{opposite}{adjacent} \implies \cfrac{b}{a} \implies \cfrac{y}{x} \\
tan\left(-\frac{3\pi}{4}\right) = \cfrac{y}{x} \implies \cfrac{y}{-1}\quad \\\quad \\
tan\left(-\frac{3\pi}{4}\right) = \cfrac{y}{-1} \implies -1\times tan\left(-\frac{3\pi}{4}\right) = y\\\quad \\\quad \\
\textit{keep in mind that } tan(-\theta) = -tan(\theta)\\\quad \\\quad \\
-1\times tan\left(-\frac{3\pi}{4}\right) = y \implies -1\times - tan\left(\frac{3\pi}{4}\right) = y \\\implies tan\left(\frac{3\pi}{4}\right) = y\)

Answer 8

so if I change 3pi/4 to degrees and calculate that in my calculator and get the tan(135)=-1 and -1(-1)=1 so my y value is 1. my coordinate is (-1,1)?

Answer 9

well, \(\bf tan\left(\frac{3\pi}{4}\right) = y\)
which is -1 rather, the negative part has already being simplified to the positive angle

Answer 10

wait the tan(-135) = 1 so 1(-1) is -1 so my y value is -1 making my coordinate (-1,-1)
oh I get it now.

Answer 11

yeap

Answer 12

THANK YOU SO MUCH!

Answer 13

yw