Question

Find sin θ if cot θ = - 4 and cos θ < 0. - 17 square root of seventeen divided by seventeen negative one divided by four square root of seventeen divided by four

Answer 1

Answer:

1/(sqrt 17), or (sqrt 17) / 17

Step-by-step explanation:

Since cot is negative, where is cot negative? Second and fourth quadrants.

Now we need to fins where cos is negative. That's easy, the second quadrant is what we are looking for. This tells us that sin is positive.

Now, if cot x = -4, that must mean that tan x = -1/4. That would be opposite over adjacent.

Since sin x requires the hypotenuse, find the hypotenuse:

z^2 = 1^2 + 4^2

z^2 = 1 + 16

z = sqrt 17

Since sin is positive, we end up with:

1/(sqrt 17), or (sqrt 17) / 17

I hope this helped.

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Answer 2

Alright, lets gets started.

We have given two things, cot Θ= - 4 and cos Θ < 0

Means both cot and cos are negative.

So, the quadrant in which Θ lies , is 2nd.

Because in 2nd quadrant, cos and cot both are negative.

Please refer the diagram attached.

Cot Θ = -4 means tan Θ = - 1/4

Means two sides, opposite = 1

adjacent = -4

We could find hypotenuse by using Pythagorean theorem.

Hypotenuse = sqrt (1^2 + -4^2) = sqrt (1+16)

Hypotenuse = √17

sin Θ = opposite / hypotenuse

sin Θ = 1/√17

Multiply and divide with √17

sin Θ = 1/√17 * √17/√17

sin Θ = √17/17 : Answer

Hope it will help :)