Question

PLEASE HELP ASAP NOW WILL MARK BRAINIEST LOTS OF POINTS!!!! HELP NOWWWWWWWWWWW 22. Explain why an sin^-1(sin(3pi/4))not equal 3pi/4 when y=sin x and y=sin ^-1 are inverses. 25. Given f(x)=sin x and g(x)= cos x, find f(g(pi/2))=0. SHOW ALL YOUR STEPS.

Answer 1

22. The range of the arcsine function (sin⁻¹(x)) is [-π/2, π/2]. The function will return π/4 for arcsin(sin(3π/4)) = arcsin(1/√2).

The sine function does not pass the horizontal line test, so it has no inverse over its entire domain. The arcsine function is only the inverse of the sine function over a limited domain/range.

25. sin(cos(π/2)) = sin(0) = 0.

As with any nested function evaluation, you evaluate the inner function first.

... cos(π/2) = 0

Then you evaluate the outer function.

... sin(0) = 0