Question

Find the exact value of the remaining trigonometric functions given: Tan x = Undefined Sin x > 0

(I’ve been having some trouble understanding this one—please explain, if possible!)

Answer 1

• sin(x) = 1
• cos(x) = 0
• cot(x) = 0
• csc(x) = 1
• sec(x) = undefined

Explanation:

The tangent function can be considered to be the ratio of the sine and cosine functions:

tan(x) = sin(x)/cos(x)

It will be undefined where cos(x) = 0. The values of x where that occurs are odd multiples of π. The smallest such multiple is x=π/2. The value of the sine function there is positive: sin(π/2) = 1.

The corresponding trig function values are ...

tan(x) = undefined (where sin(x) >0)

sin(x) = 1

cos(x) = 0

__

And the reciprocal function values at x=π/2 are ...

cot(x) = 0 . . . . . . 1/tan(x)

csc(x) = 1 . . . . . . .1/sin(x)

sec(x) = undefined . . . . . 1/cos(x)