How can we find tan inverse of a number without calculator,for eg. Tan inverse of -1 ?

1 Answer
Teddy
Jun 14, 2018

#tan^(-1)x# can be found without a calculator only for some special values of #x#.

Explanation:

For example, #tan^(-1)(-1)=-pi/4#. This is because #sin(-pi/4)=-sqrt2/2# and #cos(-pi/4)=sqrt2/2#, so #tan(-pi/4)=-1#.

In general, #tan^(-1)(x)=theta# implies that #tan(theta)=x#, remembering that #theta# can only take on values from #-pi/2# to #pi/2#. Therefore, to find #tan^(-1)x# you need to think about what value of #theta# would satisfy #tan(theta)=x#?

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