Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Trigonometric Problems and Identities
#### Exercise 10.2 Details:
- **Objective:** Solve equations involving trigonometric functions.
- **Problems:** 1-40 include multiples of 2, 6-60 multiples of 3.
#### Exercise Problems:
1. **Problem 6.**
- Equation: \( \tan \frac{\pi}{2} \)
2. **Problem 9.**
- Equation: \( \sin \left( \frac{13\pi}{12} \right) \)
3. **Problem 12.**
- Equation: \( \sin 105^\circ \)
4. **Problem 21.**
- Expression:
\[
\frac{\tan 80^\circ + \tan 85^\circ}{1 - \tan 80^\circ \tan 85^\circ}
\]
5. **Problem 24.**
- Equation: \( \sin (720^\circ + x) \)
6. **Problem 27.**
- Equation: \( \sin (x - 90^\circ) \)
7. **Problem 33.**
- Expression: \( 3 \cos \left( \frac{3\pi}{2} + x \right) \)
8. **Problem 36.**
- Equation: \( \tan (2\pi - x) \)
9. **Problem 42.**
- Equation: \( \sin \left( \frac{3\pi}{2} + x \right) \)
10. **Problem 45.**
- Equation: \( \cos 7x = \sin x \)
11. **Problem 49.**
- Expression:
\[
\cos \frac{\pi}{2} - 8 \sin x \cos x = 2 - 3\frac{\pi}{2}
\]
12. **Problem 51.**
- Trigonometric Identity:
\[
\frac{\sin(A-B)}{\sin B}, \quad \frac{\cos(A-B)}{\cos B}, \quad \frac{\sin A}{\sin B \cos B}
\]
13. **Problem 60.**
- Trigonometric Expression:
\[
\frac{\sin(x-y)}{\sin(x+y)} = \frac{\tan x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29d8e414-3c15-4fcd-af4d-5b8b723e53ca%2F71f81656-da04-47b1-81e0-2a9d9583add4%2F8a44z8j.jpeg&w=3840&q=75)
Transcribed Image Text:### Trigonometric Problems and Identities
#### Exercise 10.2 Details:
- **Objective:** Solve equations involving trigonometric functions.
- **Problems:** 1-40 include multiples of 2, 6-60 multiples of 3.
#### Exercise Problems:
1. **Problem 6.**
- Equation: \( \tan \frac{\pi}{2} \)
2. **Problem 9.**
- Equation: \( \sin \left( \frac{13\pi}{12} \right) \)
3. **Problem 12.**
- Equation: \( \sin 105^\circ \)
4. **Problem 21.**
- Expression:
\[
\frac{\tan 80^\circ + \tan 85^\circ}{1 - \tan 80^\circ \tan 85^\circ}
\]
5. **Problem 24.**
- Equation: \( \sin (720^\circ + x) \)
6. **Problem 27.**
- Equation: \( \sin (x - 90^\circ) \)
7. **Problem 33.**
- Expression: \( 3 \cos \left( \frac{3\pi}{2} + x \right) \)
8. **Problem 36.**
- Equation: \( \tan (2\pi - x) \)
9. **Problem 42.**
- Equation: \( \sin \left( \frac{3\pi}{2} + x \right) \)
10. **Problem 45.**
- Equation: \( \cos 7x = \sin x \)
11. **Problem 49.**
- Expression:
\[
\cos \frac{\pi}{2} - 8 \sin x \cos x = 2 - 3\frac{\pi}{2}
\]
12. **Problem 51.**
- Trigonometric Identity:
\[
\frac{\sin(A-B)}{\sin B}, \quad \frac{\cos(A-B)}{\cos B}, \quad \frac{\sin A}{\sin B \cos B}
\]
13. **Problem 60.**
- Trigonometric Expression:
\[
\frac{\sin(x-y)}{\sin(x+y)} = \frac{\tan x
Transcribed Image Text:### Educational Worksheet on Trigonometric Functions and Inverses
**Header Information:**
- **10.4**
- Problems: 7-10 (All), 12-42 (Every Other)
- Advanced Problems: 48-58 (Even), 60-64 (Teacher's Choice)
**Problems:**
1. **7.** \( y = \sin^{-1} x \)
- Options:
- a
- b
- c
- d
2. **8.** \( y = \cos^{-1} x \)
- Options:
- a
- b
- c
- d
3. **9.** \( y = \tan^{-1} x \)
- Options:
- a
- b
- c
- d
4. **10.**
- Options:
- a
- b
- c
**Additional Problems:**
- **12.** \( y = \sin^{-1} 0 \)
- **14.** \( y = \arctan(-1) \)
- **16.** \( y = \cos^{-1} \left(\frac{-1}{2}\right) \)
- **18.** \( y = \arcsin \left(\frac{-\sqrt{3}}{2}\right) \)
- **20.** \( y = \tan^{-1}(-\sqrt{3}) \)
- **22.** \( y = \cos^{-1} \left(\frac{-1}{2}\right) \)
**Advanced Problems:**
- **30.** \( y = \csc^{-1} \sqrt{2} \)
- **34.** \( y = \cot^{-1} 1 \)
- **36.** \( \theta = \arccos \left(\frac{-1}{2}\right) \)
**Challenge Problems:**
- **40.** \( \theta = \sec^{-1} (2) \)
- **42.** \( \theta = \csc^{-1} (1) \)
- **48.** \( \theta = \csc^{-1} (-1.324886) \)
---
This worksheet provides a series of problems involving trigonometric functions and their inverses
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