Question

<θ is in standard position with its terminal arm in the stated quadrant, and 0≤θ<2pi. A trigonometric ratio: cosθ= -2/3 is given in quadrant III. How do I find the exact values of the other two trignometric ratios?

Answer 1

There are 6 trig functions
Do you mean sin(theta) and tan(theta)?
Because there is also
csc(theta), sec(theta), cot(theta)

Answer 2

sin(theta) and tan(theta)

Answer 3

I'm having trouble reading your inequality

Answer 4

\[0 \le \theta \le 2 \pi ?\]

Answer 5

sorry , i mean 0≤θ≤2pi.

Answer 6

in quadrant III

Answer 7

Well we know the triangle can either be in quadrant 2 or 3 since we want x to be negative
since we have cos(theta)=-2/3 =(adj/hyp)

hyp is positive

Answer 8

oh its in quadrant 3 ok!

Answer 9

Find the other leg
You know Pythagorean thm

Answer 10

\[a^2+(-2)^2=3^2 \]
Solve for a to find the measurement of the opposite side of angle theta

Answer 11

Recall the following:
\[\tan(\theta)=\frac{opp}{adj} , \sin(\theta)=\frac{opp}{hyp}\]

Answer 12

a = √5
yes?

Answer 13

\[\sin(\theta)=?\]

Answer 14

oops one more thing
that y value is below the x-axis so we actually have