Question

Need some help with this math question thanks :)

Answer 1

Answer:

Option B $\frac{24}{25}$

Step-by-step explanation:

we know that

$sin(2\theta) = 2 sin(\theta) cos(\theta)$

In this problem we have

$cos(\theta)=\frac{4}{5}$

Find the value of $sin(\theta)$

Remember that

$sin^{2} (\theta)+cos^{2} (\theta)=1$

substitute the value

$sin^{2} (\theta)+(\frac{4}{5})^{2}=1$

$sin^{2} (\theta)=1-\frac{16}{25}$

$sin^{2} (\theta)=\frac{9}{25}$

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

Find the value of $sin(2\theta)$

$sin(2\theta) = 2 (\frac{3}{5})(\frac{4}{5})$

$sin(2\theta) = \frac{24}{25}$