Math Problem Statement
Solution
The question in the image asks you to find the sine of the angle given in radians, .
To solve this:
-
Identify the reference angle:
is in the fourth quadrant because when you add (full circle) to it, you get: This is equivalent to , but the angle is in the fourth quadrant. -
Determine the sine of the reference angle:
The reference angle for is itself.The sine of is:
-
Adjust for the quadrant:
Since the angle is in the fourth quadrant, the sine value is negative.Therefore:
The correct answer is .
Would you like further details or have any other questions?
Here are 5 related questions to explore further:
- What is the cosine of ?
- How would you find the tangent of ?
- What is the reference angle for an angle in the third quadrant?
- How does the sine function behave for angles in the second quadrant?
- Can you describe the process of converting an angle from degrees to radians?
Tip: When working with trigonometric functions, always consider the angle's quadrant to determine the sign of the result.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Unit Circle
Reference Angles
Formulas
sin(θ) = sin(reference angle)
Reference Angle Calculation
Sine in Fourth Quadrant
Theorems
Unit Circle Theorem
Reference Angle Theorem
Suitable Grade Level
Grades 10-12