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

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 :)

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.