Question

If sinA = -2/5 and tan θ > 0, then what are the five other trigonometric ratios?

Answer 1

`cos A = - sqrt21/5`

Explanation:

`sin A = - 2/5`. Find cos A by the identity:
`cos^2 A = 1 - sin^2 A`
`cos ^2 A = 1 - 4/25 = 21/25` ---> `cos A = +- sqrt21/5`
Since tan A > 0, then `cos A = - sqrt21/5`
`tan A = (sin A)/(cos A) = (2/5)(5/sqrt21) = 2/sqrt21`
The other trig ratios are:
`cot A = sqrt21/2`
`sec A = 1/cos A = - 5/sqrt21`
`csc A = 1/sin A = - 5/2`