Question

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

A) - 17
B) sqrt 17 / 17
C)-1/4
D) sqrt 17 / 4

Answer 1

The correct option is B

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....