Answer:
sin2θ = - [tex]\frac{24}{25}[/tex]
Step-by-step explanation:
Given
cosθ = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex] and in fourth quadrant
Then this is a 3- 4- 5 triangle with opposite side = 4
sinθ < 0 in fourth quadrant, then
sinθ = - [tex]\frac{opposite}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex]
Using the double angle identity for sine
sin2θ = 2sinθcosθ
= 2 × - [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex] = - [tex]\frac{24}{25}[/tex]
