Question: If x = sin^(-1)(1/2), what is the value of cos(x)?
Options:
1/2
β3/2
1
0
Correct Answer: β3/2
Solution:
If x = sin^(-1)(1/2), then x = Ο/6. Therefore, cos(x) = cos(Ο/6) = β3/2.
If x = sin^(-1)(1/2), what is the value of cos(x)?
Practice Questions
Q1
If x = sin^(-1)(1/2), what is the value of cos(x)?
1/2
β3/2
1
0
Questions & Step-by-Step Solutions
If x = sin^(-1)(1/2), what is the value of cos(x)?
Correct Answer: β3/2
Step 1: Understand that sin^(-1)(1/2) means we are looking for an angle x whose sine value is 1/2.
Step 2: Recall that the angle x = Ο/6 (or 30 degrees) has a sine value of 1/2.
Step 3: Now that we know x = Ο/6, we need to find cos(x).
Step 4: Use the cosine value for the angle Ο/6, which is β3/2.
Step 5: Therefore, cos(x) = β3/2.
Inverse Trigonometric Functions β Understanding how to interpret and calculate values from inverse trigonometric functions, specifically arcsine in this case.
Trigonometric Identities β Applying trigonometric identities to find the cosine of an angle derived from the sine function.
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