Math Problem Statement
Solution
The problem asks to find all values of between and for which , using the unit circle.
Solution:
We know from the unit circle that occurs at two specific angles within one full rotation (from to ):
- (30 degrees)
- (150 degrees)
These angles are in the first and second quadrants, where the sine function is positive.
Final Answer:
The two values of in the range for which are:
Would you like more details, or do you have any questions about this?
Here are 5 related questions to explore further:
- What is the value of for ?
- How would you solve in the same interval?
- What are the angles where ?
- How do you find the cosine of these angles using the unit circle?
- Can you generalize the solution for , where is any value?
Tip: Memorizing common sine and cosine values for angles like and their multiples will help solve many trigonometric problems quickly.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Unit Circle
Sine Function
Formulas
sin(θ) = opposite / hypotenuse
Values of sine function for standard angles
Theorems
Unit Circle Theorem
Sine values for angles in quadrants
Suitable Grade Level
Grades 10-12