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!