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

Answer:

Step-by-step 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

$c=\sqrt{29}$

That means that

$sin\theta=-\frac{5}{\sqrt{29} }=-\frac{5\sqrt{29} }{29}$ and

$csc\theta=-\frac{\sqrt{29} }{5}$

That means that

$cos\theta=-\frac{2}{\sqrt{29} }=-\frac{2\sqrt{29} }{29}$ and

$sec\theta=-\frac{\sqrt{29} }{2}$

It also means that

$tan\theta=\frac{5}{2}$ and

$cot\theta=\frac{2}{5}$