How do you solve the inverse trig function #cos^-1 (-sqrt2/2)#?

Answer 1

Emery Adkins

# (3pi)/4#

Find #arccos (- sqrt2/2)#. #cos x = - sqrt2/2# Trig Table and unit circle give 1 solution arc: #x = (3pi)/4#

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Answer 2

Carter Anderson

To solve the inverse trigonometric function cos^-1 (-sqrt2/2), we first recognize that the cosine function is negative in the second and third quadrants of the unit circle. Therefore, we are looking for an angle whose cosine value is -sqrt2/2. The angle that meets this criterion is -3π/4 radians or -135 degrees. Thus, cos^-1 (-sqrt2/2) = -3π/4 radians or -135 degrees.

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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.