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QA › Math › If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?

If cos Θ = negative two over five and tan Θ > 0, what is the value of sin Θ?

1. negative square root 21

2. negative square root 21 over 5

3. square root 21 over 5

4. square root of 21 over 2

Answer: 2. negative square root 21 over 5

Cos Θ = -2/5 = -0.4

Tan Θ > -1

Sin Θ = ?

Sin²Θ + Cos²Θ = 1

Sin²Θ = 1 – Cos²Θ

Sin²Θ = 1 – (–0.4)²

Sin²Θ = 1 – 0.16

Sin²Θ = 0.84

SinΘ = ± square root of 0.84

SinΘ = ±0.9165

If CosΘ is negative and TanΘ is positive, Θ lies in the third quadrant and therefore sinΘ is negative.

SinΘ = –0.9165 or negative square root of 21 over 5

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