Question

If sinB=3/4 and the terminal side of the angle is in quadrant II, how do you find the other five trigonometric functions of B?

Answer 1

`color(white)("XXXXXXXXXXXXXXXXXXXX")sec(B)4/3`
`cos(B)=-sqrt(7)/4color(white)("XXXXXXXXXX")sec(B)=4/sqrt(7)=(4sqrt(7))/7`
`tan(B)=-3/sqrt(7)=-(3sqrt(7))/7color(white)("XXXX")cot(B)=-sqrt(7)/3`

Explanation:

Setting the hypotenuse to `4` units
If `sin(B)=3/4` and `B` is in Q II
the opposite side (`y`) is `3`
and
the adjacent side (`x`) is `-sqrt(7)` (by Pythagorean Theorem)

All trigonometric functions of `B` follow directly from this.