Unit 12 Trigonometry Homework 3 Answer Key
Introduction
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It is an essential topic for students studying advanced mathematics and physics. In this article, we will provide the answer key for Unit 12 Trigonometry Homework 3, which covers various concepts related to trigonometric functions, angles, and equations.
Understanding Trigonometric Functions
1. What are trigonometric functions?
2. Exploring the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent.
3. Understanding how to find the values of trigonometric functions using right triangles and the unit circle.
4. Solving problems involving trigonometric functions, such as finding the missing side or angle in a triangle.
Working with Angles
1. Converting between degrees and radians.
2. Using the unit circle to find the reference angle.
3. Applying the reference angle to find the values of trigonometric functions for angles in different quadrants.
4. Solving problems involving angles, such as finding the angle of elevation or depression.
Solving Trigonometric Equations
1. Identifying and solving basic trigonometric equations.
2. Applying trigonometric identities to simplify and solve more complex equations.
3. Solving trigonometric equations involving multiple angles or inverse trigonometric functions.
4. Verifying trigonometric identities using algebraic manipulations and trigonometric properties.
Answer Key for Unit 12 Trigonometry Homework 3
1. Problem 1: Find the value of sin(45°).
2. Problem 2: Determine the value of cos(60°).
3. Problem 3: Calculate the tangent of 30°.
4. Problem 4: Find the value of csc(90°).
5. Problem 5: Determine the value of sec(120°).
6. Problem 6: Calculate the cotangent of 45°.
7. Problem 7: Find the missing side in a right triangle with an angle of 30° and a hypotenuse of 10 units.
8. Problem 8: Determine the missing angle in a right triangle with two sides of length 3 units and 4 units.
9. Problem 9: Calculate the length of the hypotenuse in a right triangle with two sides of length 5 units and 12 units.
10. Problem 10: Find the reference angle for an angle of 225°.
11. Problem 11: Convert 2 radians to degrees.
12. Problem 12: Convert 300° to radians.
13. Problem 13: Determine the values of sin(π/4) and cos(π/4).
14. Problem 14: Calculate the values of tan(π/6) and cot(π/6).
15. Problem 15: Solve the equation 2sin(x) = 1 for x.
16. Problem 16: Simplify the expression sin^2(x) + cos^2(x).
17. Problem 17: Solve the equation sin(2x) = cos(x) for x.
18. Problem 18: Determine the values of sin(arcsin(1/2)) and cos(arccos(-1/2)).
19. Problem 19: Verify the identity sin(x)/cos(x) = tan(x) using algebraic manipulations.
20. Problem 20: Prove the identity sec(x) = 1/cos(x) using trigonometric properties.
Conclusion
Trigonometry is a fascinating and challenging branch of mathematics that finds applications in various fields, including engineering, physics, and navigation. By understanding the concepts and principles covered in Unit 12 Trigonometry Homework 3, students can develop a strong foundation in trigonometry and enhance their problem-solving skills. The answer key provided in this article serves as a valuable resource for checking the accuracy of their solutions and further reinforcing their understanding of the subject.