2 years ago

Given sin theta=1/3 and 0 < theta< π/2; find tan 2 theta.

Mathematics

1 answer:

mote1985 [20]2 years ago

6 0

Answer:

tan2θ = 4√2/7

Step-by-step explanation:

Given sin theta=1/3 and 0 < theta< π/+

Required

tan 2 theta

tan2 theta = 2tanθ/1-tan²θ

Get tan θ

sinθ = opp/hyp

adj = √3²-1²²

adj = √9-1

adj = √8

tanθ = opp/adj = 1/2√2

tan2 theta = 2(1/2√2/1-(1/2√2)²

tan2θ = 1/√2/1-1/8

tan2θ = 1/√2/7/8

tan2θ = 8/7√2

Rationalize

tan2θ = 8√2/14

tan2θ = 4√2/7

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