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

Question

Mathematics

Kyson Trevino

23 March, 00:00

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

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Answers (1)

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Rambo · Answer 1

Sin² Θ + cos² Θ = 1

sin² Θ + (-2/5) ² = 1

sin² Θ + (4/25) = 1

sin² Θ = 21/25

sin Θ = ± (√21) / 5

cos Θ is negative and tan Θ is positive, so Θ must be in the third quadrant, and sin Θ must be negative.

sin Θ = (√21) / 5