Question

If cos0=3/5 and θ is in quadrant IV, sin20=?

Answer 1

Answer:

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

Step-by-step explanation:

We know that $cos(\theta) =\frac{3}{5}$ and θ is in quadrant IV

To find $sin(\theta)$ we use the following identity

$sin^2(\theta)=1-cos^2(\theta)$

$cos^2(\theta) =\frac{3^2}{5^2}$

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

Then

$sin^2(\theta)=1-\frac{9}{25}$

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

$sin(\theta)=\±\sqrt{\frac{16}{25}}$

In the IV quadrant the $sin(\theta)> 0$ then we take the positive solution

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

Finally to find  $sin(2\theta)$ we use the following identity

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

Finally

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

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