If sin(x) = 0.5, what are the possible values of x in degrees?

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Question: If sin(x) = 0.5, what are the possible values of x in degrees?

Options:

Correct Answer: 30°, 150°

Solution:

sin(x) = 0.5 gives x = 30° and 150°.

If sin(x) = 0.5, what are the possible values of x in degrees?

If sin(x) = 0.5, what are the possible values of x in degrees?

Step 1: Understand that sin(x) = 0.5 means we are looking for angles where the sine value is 0.5.
Step 2: Recall that the sine function is positive in the first and second quadrants of the unit circle.
Step 3: Identify the first angle where sin(x) = 0.5, which is 30 degrees.
Step 4: Find the second angle in the second quadrant where sin(x) = 0.5. This angle is 180 degrees - 30 degrees, which equals 150 degrees.
Step 5: Conclude that the possible values of x are 30 degrees and 150 degrees.

Trigonometric Functions – Understanding the sine function and its values on the unit circle.
Inverse Trigonometric Functions – Using the inverse sine function to find angles corresponding to specific sine values.
Periodic Nature of Trigonometric Functions – Recognizing that sine is periodic and can have multiple solutions within a given range.