Question

How do you find the five remaining trigonometric function satisfying `sintheta=3/8`, `costheta<0`?

Answer 1

`cosΘ=(-√55)/8`
`tanΘ=(-3√55)/55`
`cscΘ=8/3`
`secΘ=(-8√55)/55`
`cotΘ=(-√55)/3`

Explanation:

Since `sin` is positive and `cos` is less than 0, it means that this triangle is in quadrant 2.

Use Pythagorean's theorem (`a^2+b^2=c^2`) and plug in your given values: `a=3` and `c=8` and solve.

`3^2+b^2=8^2` → `9+b^2=64` → `b^2=55` → `b=-√55` (it is negative because it is in quadrant 2 and the `cos` is the x value of the triangle)

Now that you have all side lengths, simply plug them in to the remaining trigonometric functions:

`cosΘ=(-√55)/8`
`tanΘ=3/(-√55)=(-3√55)/55`
`cscΘ=8/3`
`secΘ=8/(-√55)=(-8√55)/55`
`cotΘ=(-√55)/3`