Given that csc(θ)=5/2 and π/2 <θ< π, find cot(θ).

Answer 1

If csc x = 5/2 = hypotenuse/opposite

cot x = adjacent/opposite

we need to find the adjacent side, using the Pythagorean Theorem

√(5²-2²) = √21

cot = -√21/2

(negative because tan is negative in the second quadrant)

Answer 2

sin = 1/csc = 2/5

Draw a right triangle with hypotenuse = 5

(Sorry, I can't draw in this answer area.)

Easier to work in first quadrant

Sides of triangle (x,y,h) = (x,2,5)

Use pythagorean theorem to find x = sqrt(21)

Now, it's easy to see tan = 2 / sqrt(21)

And the cot = sqrt(21) / 2

Now, move to the second quadrant

Here, cot = - sqrt(21) / 2