Question

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

Answer 1

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 = $\frac{63}{225}$ = $\frac{7}{25}$