Math Problem Statement
Solution
The problem asks for values of where within the interval .
Step 1: Solve
The general solution for is: for any integer , since these angles correspond to where .
Step 2: Find values of in the interval
We need to convert the upper bound to a more comparable form: Thus, the interval is approximately (in radians).
Step 3: Determine specific values
By adding or subtracting multiples of , we will determine which solutions fall into the given interval.
Let me calculate this for you.The values of that satisfy within the interval are approximately:
These correspond to angles where the sine function equals in the given interval.
Would you like further details or have any questions?
Here are 5 related questions to expand on the topic:
- What is the general solution for the equation ?
- How do we determine the period of trigonometric functions like sine and cosine?
- What is the reference angle for the sine function in the unit circle?
- How do we solve within a specified interval?
- Can you explain how to convert radians to degrees and vice versa?
Tip: When solving trigonometric equations over intervals, remember to adjust for the periodic nature of the function by considering all solutions that fall within the interval.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Sine Function
Unit Circle
Solving Trigonometric Equations
Formulas
sin(x) = -1/2
General solution for sine: x = nπ + (-1)^n * arcsin(value)
Theorems
Periodic nature of sine function
General solution of sine equations
Suitable Grade Level
Grades 9-12