If tan theta=2/3,find theta?

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Answer 1 · 2018-06-25T06:36:26

#theta approx 0.5880+npi: n in ZZ#

#tan theta=2/3#

#:. theta = arctan(2/3)#

We can use a calculator to find the primary value of #theta in [0,pi/2]#

#theta approx 0.5880#

#tan theta# is also equal #2/3# for #theta approx 0.5880 +npi: n in ZZ#

We can visualise this from the graphic below showing the intersections between #y=tanx and y=2/3#

graph{(y-tanx)(y-0x-0.667)=0 [-7.024, 7.02, -3.51, 3.514]}