Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
5. Inverse Trigonometric Functions and Basic Trigonometric Equations
Inverse Sine, Cosine, & Tangent
Problem 6.45a
Textbook Question
Solve each equation for exact solutions.
arcsin 2x + arccos x = π/6
Verified step by step guidance
1
Identify the domain of the functions involved. Recall that the domain of arcsin(u) is -1 ≤ u ≤ 1 and for arccos(u) is -1 ≤ u ≤ 1. Therefore, ensure that 2x and x fall within these ranges.
Rewrite the equation in terms of a single trigonometric function. You can use the identity sin(θ) = cos(π/2 - θ) to express arccos(x) as π/2 - arcsin(x).
Substitute arccos(x) in the original equation: arcsin(2x) + π/2 - arcsin(x) = π/6.
Simplify the equation to isolate terms involving arcsin. This can be done by subtracting π/2 from both sides and then simplifying further.
Solve the resulting equation for x. This might involve using trigonometric identities or inverse trigonometric properties to find the values of x that satisfy the equation within the defined domain.
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