what r the remaining five trig values?

Question

If the csc(theta)= -(10/8) and theta is in quad 2, what r the remaining five trig values?

Answer 1

This is impossible, since the hypotenuse is always positive and in quadrant 2 the opposite side (y) is positive. In quadrant 2, a negative cosecant can't come from anything.

I can show you the solution for quadrant 4 though, where the opposite side (y) is negative and the adjacent side (x) is positive. We're given csc(theta) = -10/8. Cosecant of x is equal to 1/sinx, and 1/sinx is hypotenuse/opposite. So the opposite (y) must be -8, and the hypotenuse must be 10.

We can use the pythagorean theorem to find the opposite(x) side, where opp^2 + adj^2 = hyp^2.

(-8)^2 + adj^2 = 10^2

64 + adj^2 = 100

adj^2 = 36

adj = + or - 6.

We're in quadrant 4, so adj has to be positive. Our answer is adj = 6.

To sum up:

adj = 6

opp = -8

hyp = 10

Now we can find the remaining trig values.

Sin(theta) = opp/hyp = -8/10 = -0.8

Cos(theta) = adj/hyp = 6/10 = 0.6

Tan(theta) = opp/adj = -8/6 = -1.33

Sec(theta) = hyp/adj = 10/6 = 1.67

Cot(theta) = adj/opp = 6/-8 = -0.75