Question

How do you find the remaining trigonometric functions of `theta` given `tantheta=3/4` and `theta` terminates in QIII?

Answer 1

`3/5,5/3,4/5,5/4,4/3`

Explanation:

We know tan`theta` = 3/4 = height/base of a right angle triangle.

Hence, hypotenuse = `sqrt(base^2 + height^2)` = `sqrt(4^2+3^2)`

= `sqrt 25 = 5`

Hence sin`theta = ("height")/("hypotenuse") = -3/5`
cosec`theta = 1/sintheta= -5/3`.
cos`theta =("base")/("hypotenuse") = -4/5`
sec`theta =1/costheta = -5/4`
cot`theta = 1/tantheta = 4/3`