What is the range of the function y = cos^(-1)(x)?
Practice Questions
Q1
What is the range of the function y = cos^(-1)(x)?
[0, π]
[0, 2π]
[−π/2, π/2]
[−1, 1]
Questions & Step-by-Step Solutions
What is the range of the function y = cos^(-1)(x)?
Correct Answer: [0, π]
Step 1: Understand what the function y = cos^(-1)(x) means. This is the inverse cosine function, which gives you an angle whose cosine is x.
Step 2: Know that the cosine function (cos) takes angles and gives values between -1 and 1. Therefore, the input x for the inverse cosine function must be between -1 and 1.
Step 3: Recognize that the output of the inverse cosine function (y) is an angle. We need to find out what angles correspond to the values of x between -1 and 1.
Step 4: The inverse cosine function gives angles from 0 to π (0 to 180 degrees). This means that for any value of x in the range [-1, 1], the output y will be between 0 and π.
Step 5: Conclude that the range of the function y = cos^(-1)(x) is [0, π].
