Question

if sin=3/5 then what does tan equal

Answer 1

Answer: $tan(x)=\±\frac{3}{4}$

Step-by-step explanation:

You know that $sin(x)=\frac{3}{5}$ and you can identify that. Then:

$sin^2(x)=(\frac{3}{5})^2$

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

Remember that:

$cos^2(x)=1-sin^2(x)$

Then $cos^2(x)$ is:

$cos^2(x)=1-\frac{9}{25}\\\\cos^2(x)=\frac{16}{25}$

Apply square root to both sides to find cos(x):

$\sqrt{cos^2(x)}=\±\sqrt{\frac{16}{25}}\\cos(x)=\±\frac{4}{5}$

Remember that:

$tan(x)=\frac{sin(x)}{cos(x)}$

Then, this is:

$tan(x)=\frac{\frac{3}{5}}{\±\frac{4}{5}}$

$tan(x)=\±\frac{3}{4}$