Answer:
sin2θ = [tex]\frac{1320}{3721}[/tex]
Step-by-step explanation:
Given
sinθ = [tex]\frac{11}{61}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a right triangle with legs 11 and x ( adjacent ) and hypotenuse 61
Using Pythagoras' identity in the right triangle to find x
x² + 11² = 61²
x² + 121 = 3721 ( subtract 121 from both sides )
x² = 3600 ( take the square root of both sides )
x = [tex]\sqrt{3600}[/tex] = 60
Then cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{60}{61}[/tex]
Using the identity
sin2θ = 2sinθcosθ , then
sin2θ = 2 × [tex]\frac{11}{61}[/tex] × [tex]\frac{60}{61}[/tex] = [tex]\frac{1320}{3721}[/tex]
