How do you evaluate #sec^-1(sec((7pi)/10))#?

Answer 1

#(7pi)/10#

#sec^(-1)x# is defined for x#in(R-]-1,1[)rarr([0,pi]-{pi/2})#. #sec^(-1)secx= x# if and only if x#in([0,pi]-{pi/2})#. in your question, since #(7pi)/10in([0,pi]-{pi/2})# so, #sec^(-1)sec((7pi)/10)=(7pi)/10#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Delilah Aguilar

To evaluate ( \sec^{-1}(\sec\left(\frac{7\pi}{10}\right)) ), you apply the inverse secant function to the secant of ( \frac{7\pi}{10} ). Since the secant function returns the ratio of the hypotenuse to the adjacent side in a right triangle, you can draw a right triangle with angle ( \frac{7\pi}{10} ) and find the adjacent side and hypotenuse. Then, you can use the inverse secant function to find the angle whose secant is ( \frac{7\pi}{10} ).

By signing up, you agree to our Terms of Service and Privacy Policy

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.