Question

Use the figure below to determine the exact value of the given function sin2 0

Answer 1

Answer:

sin2θ = $\frac{12}{13}$

Step-by-step explanation:

Since, sin2θ = 2sinθcosθ

From the triangle given in the picture,

Opposite side of angle θ = 2 units

Adjacent side of angle θ = 3 units

Hypotenuse = $\sqrt{2^2+3^2}$ = $\sqrt{13}$ [By Pythagoras theorem]

sinθ = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

       = $\frac{2}{\sqrt{13}}$

cosθ = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

        = $\frac{3}{\sqrt{13} }$

sin2θ = $2\times (\frac{2}{\sqrt{13}})(\frac{3}{\sqrt{13}})$

         = $\frac{12}{13}$