Question

If sin theta = 4/5 and theta is in quadrant 2, the value of cot theta is

Answer 1

cotθ = -3/4

Explanation:

Given:

sinθ = 4/5

θ is in Quadrant II, so cosθ < 0

Recall:

cotθ = cosθ/sinθ

cos²θ + sin²θ = 1

Determine cosθ:

cosθ = -√(1-sin²θ) = -√(1-(4/5)²) = -√(1-16/25) = -√(9/25) = -3/5

Determine cotθ:

cotθ = cosθ/sinθ = (-3/5)/(4/5) = (-3/5)(5/4) = -15/20 = -3/4

Answer 2

Cot(theta) = - 0.75 or -3/4

Explanation:

The hypotenuse is 5

The y value is 4

We need to find the corresponding x value.

x^2 + y^2 = z^2

X = ?

y = 4

z = 5

x^2 + 4^2 = 5^2

x^2 + 16 = 25

x^2 = 9

Now in this case, you are in quadrant 2, so the x value is - 3

sqrt(x^2) = sqrt(9)

x = - 3

The cot value is the adjacent (x value) / the opposite ( y ) value

Cot(theta) = -3/4

cot(theta) = -0.75