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How do you find the exact values of #sintheta# and #tantheta# when #costheta=0#?

Answer 1

Violet Anderson

#simtheta=+-1# and #tantheta# is not defined.

As #costheta=0#, we have

#sintheta=sqrt(1-cos^2theta)=sqrt(1-0)=sqrt1=+-1# and

#theta=+-pi/2#

But, #tantheta=sintheta/costheta# and as #sintheta!=0#, but #costheta=0#, #tantheta# is not defined.

However, as #theta->pi/2# from left (on real number line), #tantheta->oo# and as #theta->pi/2# from right (on real number line), #tantheta->-oo#.

Similarly, as #theta->-pi/2# from left (on real number line), #tantheta->oo# and as #theta->-pi/2# from right (on real number line), #tantheta->-oo#. graph{tanx [-10, 10, -5, 5]}

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Answer 2

Abigail Armstrong

When cos(theta) = 0, sin(theta) = ±1 and tan(theta) is undefined.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.