Answer:
see explanation
Step-by-step explanation:
using the trigonometric identities
• sin2x = 2sinxcosx
• cos2x = 2cos²x - 1
• sin²x + cos²x = 1
sinx = ± [tex]\sqrt{1-cos^2x}[/tex]
= ± [tex]\sqrt{1-(-12/15)^2}[/tex]
= ± [tex]\sqrt{1-\frac{144}{225} }[/tex]
= ± [tex]\sqrt{\frac{81}{225} }[/tex] = ± [tex]\frac{9}{15}[/tex]
since sinΘ > 0 then sinΘ = [tex]\frac{9}{15}[/tex] = [tex]\frac{3}{5}[/tex]
sin2Θ = 2 × [tex]\frac{3}{5}[/tex] × - [tex]\frac{12}{15}[/tex] = - [tex]\frac{24}{25}[/tex]
cos2Θ = 2 × (- [tex]\frac{12}{15}[/tex])² - 1
= 2 × [tex]\frac{144}{225}[/tex] - 1
= [tex]\frac{288}{225}[/tex] - 1 = [tex]\frac{63}{225}[/tex] = [tex]\frac{7}{25}[/tex]
