Question: If x = cos^(-1)(1/2), then the value of sin(x) is:
Options:
1/2
β3/2
1
0
Correct Answer: β3/2
Solution:
If x = cos^(-1)(1/2), then x = Ο/3. Therefore, sin(x) = sin(Ο/3) = β3/2.
If x = cos^(-1)(1/2), then the value of sin(x) is:
Practice Questions
Q1
If x = cos^(-1)(1/2), then the value of sin(x) is:
1/2
β3/2
1
0
Questions & Step-by-Step Solutions
If x = cos^(-1)(1/2), then the value of sin(x) is:
Step 1: Understand that cos^(-1)(1/2) means we are looking for an angle x whose cosine value is 1/2.
Step 2: Recall the unit circle or the values of cosine for common angles. The angle x that has a cosine of 1/2 is Ο/3 (or 60 degrees).
Step 3: Now that we have x = Ο/3, we need to find sin(x).
Step 4: Use the known value of sin(Ο/3). From trigonometric values, sin(Ο/3) = β3/2.
Step 5: Therefore, the value of sin(x) is β3/2.
Inverse Trigonometric Functions β Understanding how to use inverse trigonometric functions to find angles and their corresponding sine or cosine values.
Trigonometric Values of Special Angles β Knowledge of the sine and cosine values for common angles such as Ο/3, Ο/4, and Ο/6.
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