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How do you evaluate #cot (cos^-1(-0.7003))#?

Answer 1

Madelyn Adams

#- .981830523#, nearly

Let #a = cos^(-1)(-.7003) in Q2#, for principal value. In Q2, cotangent

is positive.

The given expression is

#cot a#

# = cos a/sin a#

#= -.7003/sqrt(1-(-.7003)^2)#

#=- .981830523#, nearly..

Had we allowed other values of a in Q3,, wherein cot a is positive,

# cot a=.981830523#, nearly..

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Answer 2

Oliver Atkinson

To evaluate cot(cos^(-1)(-0.7003)), first find the corresponding angle for cos^(-1)(-0.7003). Then, find the cotangent of that angle.

Start by finding the angle whose cosine is -0.7003. You can do this using a calculator or by using the inverse cosine function.
Once you have the angle, calculate the cotangent of that angle using the formula cot(x) = 1/tan(x), where x is the angle.

So, evaluate cos^(-1)(-0.7003) to find the angle, then find the cotangent of that angle.

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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.