Question

Suppose tan(θ) is undefined and sin(θ) < 0. Find the exact values of the 6 trigonometric functions of the angle θ?

Suppose tan(θ) is undefined and sin(θ) < 0. Find the exact values of the 6 trigonometric functions of the angle θ.

Answer 1

`sin((3pi)/2)=-1`
`cos((3pi)/2) = 0`
`tan((3pi)/2)` is undefined
`csc((3pi)/2) = -1`
`sec((3pi)/2)` is undefined
`cot((3pi)/2) = 0`

Explanation:

Since the tangent is undefined, we must assume that `cos(theta)=0`. this only happens if `theta = pi/2` or `theta=(3pi)/2`

But we also know that `sin(theta)<0`. Since `sin(pi/2)=1` and `sin((3pi)/2)=-1`, we know that `theta=(3pi)/2`.