SOLUTION: If tant=−8/15 and 3 π/2 < t < 2 π , find sint , cost , sect , csct , cott .

Question 1198928: If tant=−8/15 and 3 π/2 < t < 2 π , find sint , cost , sect , csct , cott .
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

I'll use theta in place of the variable t
theta = = Greek letter often used with angles

tan(theta) = -8/15
tan(angle) = opposite/adjacent
opposite = -8
adjacent = 15

Use the pythagorean theorem to find the hypotenuse is 17 units
Pythagorean theorem is

We can form this diagram

The angle theta is in quadrant Q4 since 3pi/2 < theta < 2pi, where theta is in radians.

Then recall these trig ratios
sin(theta) = opposite/hypotenuse
cos(theta) = adjacent/hypotenuse
tan(theta) = opposite/adjacent

and we have these reciprocal ratios as well
csc(theta) = 1/sin = hypotenuse/opposite
sec(theta) = 1/cos = hypotenuse/adjacent
cot(theta) = 1/tan = adjacent/opposite

I'll let you finish things up.

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