How do you evaluate #tan^-1(0)# without a calculator?

1 Answer
Shell
Dec 1, 2016

#theta=0#

Explanation:

Find #tan^-1 (0)# without a calculator.

#tan^-1(0)# refers to the ANGLE whose tangent equals zero.

Recall the identity #tantheta = sintheta/costheta#

If #tantheta=0#, then the numerator of #sintheta/costheta# must also equal zero.

So, #sintheta"=0#.

Referring to the unit circle, the angles with a sine of zero are
#theta =0, pi#.

BUT, IT'S A BIT MORE COMPLICATED!

The range of #tan^-1# (also called arctan) is #-pi/2# to #pi/2#.

In other words, the only "allowed" values of #tan^-1# fall within this range. So, the the answer #theta=pi# is not allowed, and the answer to the problem #tan^-1(0)# is #theta=0#

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