Math Problem Statement
Sin^-1(sin7pi/6)
Solution
To solve , we first simplify .
- is in the third quadrant, where sine is negative.
- The reference angle for is , so:
Now, we need to find . The principal value of the inverse sine function, , returns values in the range . The angle in this range whose sine is is .
Thus:
Would you like further details or have any questions?
Here are 5 related questions:
- How do you determine the reference angle for any given angle?
- What are the properties of the inverse sine function?
- How do you convert between radians and degrees for trigonometric functions?
- What are the sine values for standard angles in all four quadrants?
- How does the unit circle help in solving trigonometric equations?
Tip: Always remember the range of the inverse sine function is , so it only gives values from the first and fourth quadrants.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Trigonometry
Inverse Trigonometric Functions
Unit Circle
Reference Angle
Formulas
sin(θ) = opposite/hypotenuse
sin^-1(x) is the inverse sine function
Range of sin^-1: [-π/2, π/2]
Theorems
Reference Angle Theorem
Principal Value Theorem for Inverse Trigonometric Functions
Suitable Grade Level
Grades 10-12