Question

if TanA=3/4, find the value of Sin3A​

Answer 1

Answer:

$\frac{117}{125}$

Step-by-step explanation:

$\tan( \alpha ) = \frac{3}{4}$

Using the 3,4,5 triangle, we get:

$\sin( \alpha ) = \frac{3}{5}$

There is a formula for sin(3x):

$\sin(3 \alpha ) = 3 \sin( \alpha ) - 4 sin^{3} ( \alpha )$

$\sin(3 \alpha ) = \frac{9}{5} - \frac{108}{125}$

$\sin(3 \alpha ) = \frac{225 - 108}{125}$

$\frac{117}{125}$

Answer 2

Answer:117/125

Step-by-step explanation: TanA is 3/4 so by Pythagoras theorem hypotenuse is 5. so SinA=3/5 and cosA=4/5

Sin3A=sin(2A+A)=sin2A.CosA+Cos2A.SinA

Sin2A=2sinA.Cos2A=24/25

Cos2A=cos^2 A-sin^2 A=7/25

Now sin3A= 24/25.4/5+7/25.3/5=117/125