Given $sin theta=3/5$ and $cos theta=4/5$ , how do you find $tan theta$ ?

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Answer 1 · 2016-06-10T13:42:53

$tan theta = 3/4$

Recall the quotient identity $tanx = sinx/cosx$

$tantheta = sinx/cosx$

$tantheta = (3/5)/(4/5)$

$tantheta = 3/5 xx 5/4$

$tantheta = 3/4$

Note you could have also said that

$sintheta = "opposite"/"hypotenuse"$ , $costheta = "adjacent"/"hypotenuse"$ and $tantheta = "opposite"/"adjacent"$ .

If we know that $sintheta = 3/5$ , the side opposite $theta$ measures 3.

If we know that $costheta = 4/5$ , the side adjacent $theta$ metres 4.

Applying the definition of $tantheta = "opposite"/"adjacent"$ , we have that $tantheta = 3/4$

Hopefully this helps!

Given sin theta=3/5sin theta=3/5 and cos theta=4/5cos theta=4/5, how do you find tan thetatan theta?