Find sin θ if cot θ = - 4 and cos θ < 0.

A) - 17

B) sqrt 17 / 17

C) - 1/4

D) sqrt 17 / 4

The correct option is B

Step-by-step explanation:

The correct option is B.

Solution:

We have given that

cot θ = - 4

cos θ < 0

This shows that both the ratios are negative. So they lie in second quadrant because both are negative.

cot θ = - 4 it means that tan θ = - 1/4 which shows that two sides opposite = 1 and adjacent = - 4

Now we could find hypotenuse by Pythagorean theorem:

Hypotenuse = √ (1) ² + (-4) ² = √1+16

=√17

Sin θ = perpendicular (opposite) / hypotenuse

Sin θ = 1/√17

Now multiply and divide by √17

Sin θ = 1/√17*√17/√17

Sin θ = √17/17

Thus the correct option is B ...