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kherson [118]
3 years ago
7

Use identities to find sin2Θ and cos2Θ, given cosΘ= -12/15 and sinΘ>0 PLZ HELP ASAP

Mathematics
1 answer:
Kazeer [188]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

using the trigonometric identities

• sin2x = 2sinxcosx

• cos2x = 2cos²x - 1

• sin²x + cos²x = 1

sinx = ± \sqrt{1-cos^2x}

       = ± \sqrt{1-(-12/15)^2}

       = ± \sqrt{1-\frac{144}{225} }

       = ± \sqrt{\frac{81}{225} } = ± \frac{9}{15}

since sinΘ > 0 then sinΘ = \frac{9}{15} = \frac{3}{5}

sin2Θ = 2 × \frac{3}{5} × - \frac{12}{15} = - \frac{24}{25}

cos2Θ = 2 × (- \frac{12}{15})² - 1

           = 2 × \frac{144}{225} - 1

           = \frac{288}{225} - 1 = \frac{63}{225} = \frac{7}{25}

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