Answer:
- [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
Using the double angle identity
sin2x = 2sinxcosx and
sin²x + cos²x = 1 ⇒ sinx = ± [tex]\sqrt{1-cos^2x}[/tex]
Since Θ is in fourth quadrant then sinΘ < 0
sinΘ =- [tex]\sqrt{1-(3/5)^2}[/tex]
= - [tex]\sqrt{1-9/25}[/tex]
= - [tex]\sqrt{25/25-9/25}[/tex]
= - [tex]\sqrt{\frac{16}{25} }[/tex] = - [tex]\frac{4}{5}[/tex]
Hence
sin2Θ = 2 × - [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex] = - [tex]\frac{24}{25}[/tex]
