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Question

Find sin2x, cos2x, tan2x if sinx = -1/√5 and x terminates in quadrant IV.

Sin2x=??

Cos2x=??

Tan2x=??

Answer 1

sin x = -1/√5 is illustrated below that terminates in quadrant 4:

a=((√5)²-(-1)²)^1/2

a= 2

Therefore:

cos x = 2 /√5

tan x = -1/2

Using double angle formula:

sin2x = 2 sinx cosx = 2 (-1/√5)(2/√5) = -4/5

cos2x = 1- 2sin²x = 1- 2(-1/√5)² = 1 - 2/5 = 3 / 5

tan2x = 2 tanx/ (1-tan²x) = 2(-1/2)/(1-(-1/2)²) = -1/(1-1/4) = -1/(3/4) = -4/3