If cot t = -24/7, tan t is the reciprocal, or -7/24.
You can use the trig identity: 1 + tan^2 t = sec^2 t
So 1 + 49/576 = 625/576 = sec^2 t, so sec t = 25/24
cos t is the reciprocal of sec t, so cos t = 24/25
sin^2 t + cos^2 t = 1, so sin^2 t = 1 - cos^2 t = 1 - (576/625) = 49/625 = sin^2 t
so sin t = 7/25, csc t is the reciprocal of sin t so csc t = 25/7
For the quadrants just change the signs of the values found.
a. Now if t lies in the 2nd Quadrant, sin is positive, cos is negative and tan is sin/cos (pos/neg) which is negative.
cot = -24/7, tan = -7/24, cos = -24/25, sec t = -25/24, sin = 7/25, csc = 25/7
b. If t lies in the 4th Quadrant, sin is negative and cos is positive and tan is negative.
cot = -24/7, tan = -7/24, cos = 24/25, sec t = 25/24, sin = -7/25, csc = -25/7
Well, you need to find "r" because Quad. 2 is going to be under the sine quadrant. The sine Quadrant is basicly y/r, similarly the tangent quadrant (which is what your provided with) is y/x
So basicly. r= x^2 + y^2
Sub in positive numbers, when doing these calcuations. So +24 not -24
Once you get your answer, IF it square root's to a whole number (ex. 1, 2...so on) then that is your "r" value, if when you square it you get decimal answers (ex. 3.433...) then just use your original answer from your calculation (ex. √23 or whatever value you got)
So after you do that, you have your x,y and r values.
Quad 2, is y/r
Quad 4 is x/r
sub in the values and your done.