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Allisa [31]
3 years ago
8

Find cos θ if sin θ = -(5/13) and tan θ > 0

Mathematics
2 answers:
kakasveta [241]3 years ago
4 0

Answer:

cos\theta =-\frac{12}{13}

Step-by-step explanation:

tan\theta =\frac{sin \theta}{cos \theta}

If tan θ > 0 and sin θ < 0 then cos θ <0

We have sin²θ + cos²θ = 1

That is

           \left ( \frac{-5}{13} \right )^2+cos^2\theta =1\\\\cos^2\theta =1-\frac{25}{169}=\frac{144}{169}\\\\cos\theta =-\frac{12}{13}

Nostrana [21]3 years ago
3 0
Remember:

sin²x + cos²x = 1

(-5/13)² + cos²<span>θ = 1

(25/169) + cos²</span><span>θ = 1

cos²</span><span>θ = 1 - (25/169)

cos²</span><span>θ = (144/169)

tan </span>θ > 0 ⇒ cos<span>θ = negative

cos</span>θ = -√(144/169)

cos<span>θ = -(12/13)</span>
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