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

The answer is b) classify the triangle in two different ways...

Use the figure below to determine the exact value

saabrrinnaaa

30.04.2021

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

= $\frac{12}{13}$

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