Question

If sin(x) = k and 0 < x < 90°, what is the value of cot(x)?

Answer 1

Knowing that the angle x is in the first quadrant (between 0 and 90 degrees) we are asked to find the value of the cot(x).

We recall that cot(x) is defined as the quotient of cos(x) divided sin(x)

We know that sin(x) is k, so we know the denominator. We need to find the value of cos(x) which we do via the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

k^2 + cos^2(x) = 1

cos^2(x) = 1 - k^2

Now for expressing the square root, I am going to use the equation editor:

`\cos (x)=\sqrt[]{1-k^2}`

Then, the value of the cot(x) (which by the way must be positive because we are dealing with an angle in the first quadrant) is written as:

`\cot (x)=\frac{\sqrt[]{1-k^2}}{k}`