Question

How do you use the point `(-3,-4)` on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

The ratios tan and cot are positive, all the others are negative.

The angle we are dealing with is 233.1°

Explanation:

From the given point, we can deduce the following.

The point is in the 3rd quadrant. The right-angled triangle which is formed has a hypotenuse of length 5.

Angles in the third quadrant are from 180° to 270°.

Instead of referring to the sides as opposite, adjacent and hypotenuse, we will use them as a y-component, an x-component and the radius.

The trig ratios are as follows

`sin theta= o/h = y/r = -4/5" "rArr sin theta` is negative

`cos theta= a/h = x/r=-3/5 " "rArr cos theta` is negative

`tan theta= o/a = y/x = 4/3" "rArr tan theta` is positive

`cot theta= a/o = x/y = 3/4 " "rArr tan theta` is positive

`sec theta= h/a =r/x =5/-3 " "rArr cot theta` is negative

`"cosec " theta = h/o = r/y =5/-4" "rArr" cosec " theta` is negative

In this case `theta = 180° +53.1 = 233.1°`