Question

A point on the terminal side of an angle theta is given. Find the exact value of each of the six trigonometric functions of theta. (-2,-5) sin theta = cos theta = tan theta = csc theta = sec theta = cot theta =

Answer 1

Explanation:

Plot that point in the x/y coordinate plane to see that it sits in the third quadrant. From the point, draw a line to the origin, constructing a right triangle. The side adjacent to the angle is -2, the side across from the angle is -5, so we need to find the length of the hypotenuse using Pythagorean's Theorem:

`c^2=(-5)^2+(-2)^2` and

`c^2=25+4` so

`c=√(29)`

That means that

`sin\theta=-(5)/(√(29) )=-(5√(29) )/(29)` and

`csc\theta=-(√(29) )/(5)`

That means that

`cos\theta=-(2)/(√(29) )=-(2√(29) )/(29)` and

`sec\theta=-(√(29) )/(2)`

It also means that

`tan\theta=(5)/(2)` and

`cot\theta=(2)/(5)`