If sin=3/5 then what does tan equal

Question

asked Nov 18, 2020 222k views

2 Answers

Walton · Answer 1 · 2020-11-25T12:46:35+0000

Answer:
$tan(x)=\±(3)/(4)$

Explanation:

You know that
sin(x)=(3)/(5) and you can identify that. Then:

sin^2(x)=((3)/(5))^2

sin^2(x)=(9)/(25)

Remember that:

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

Then
cos^2(x) is:

$cos^2(x)=1-(9)/(25)\\\\cos^2(x)=(16)/(25)$

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

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

Remember that:

tan(x)=(sin(x))/(cos(x))

Then, this is:

$tan(x)=((3)/(5))/(\±(4)/(5))$

$tan(x)=\±(3)/(4)$