Question

If cscx= (4√3)/3 and cosx<0, find sin x

Answer 1

Using trig definitions and identities:

1. sin x = 1/csc x = 1/3

2. cos²x = 1 - sin²x = 1 - 1/9 = 8/9.
Since cos x < 0 we take the negative square root: cos x = -(√8)/3 = -2(√2)/3.

3. tan x = sin x/cos x = (1/3) / -2(√2)/3 = -1/(2√2) = -(√2)/4.

4. cot x = 1/tan x = -2√2.

5. sec x = 1/cos x = -3/(2√2) = -3(√2)/4

Answer 2

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