Find the values of the inverse function in radians. 1. sin^-1(0.65)?

answer choices:

a. 0.71+2pi n and -0.71+2pi n
b. 0.71+2pi n and -3.85+2pi n
c. 0.86+2pi n and -0.86 +2pi n
d. -0.61+2pi n and 2.54+2pi n

My answer is B

Nope. Those answers are in QI and QIV

The solutions are in QI and QII:

sin(.71) = .65
so the solutions are

.71 + 2nπ
pi-.71 + 2nπ = 2.4 + 2nπ

The primary solutions are

.71 and π-.71
or
.71 and 2.43

so I would state it as
.71 + 2πn and 2.43 + 2πn , which is a variation of B

so you are correct, but I find their choice puzzling
(notice -3.85 + 2π = 2.43)

thank you

To find the value of the inverse function sin^-1(0.65) in radians, you need to use the inverse sine function, also known as arcsine. The arcsine function returns the angle whose sine equals the given input.

To find the answer, follow these steps:

1. Use a calculator or a reference table to find the arcsine of 0.65. Make sure your calculator is set to radians mode.

2. By calculating arcsine(0.65), you should get approximately 0.71 radians.

Now that you have determined the value of the inverse function in radians, let's match it with the answer choices:

Answer choice a: 0.71+2πn and -0.71+2πn
Answer choice b: 0.71+2πn and -3.85+2πn
Answer choice c: 0.86+2πn and -0.86+2πn
Answer choice d: -0.61+2πn and 2.54+2πn

Comparing the calculated value of 0.71 radians with the answer choices, you can see that answer choice b (0.71+2πn and -3.85+2πn) matches the value obtained.

Therefore, the correct answer is b.