Use the sum and double angle identities to write cos 3x in terms of cos x: Cos 3x = + cos°x + + cos?x + COS X

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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The drop down options are 1 through -9 as pictured for all the drop downs.
**Transcription:**

**Title: Using Trigonometric Identities**

**Instructions:**
Use the sum and double angle identities to write \(\cos 3x\) in terms of \(\cos x\):

\[
\cos 3x = \square \cos^3 x + \square \cos^2 x + \square \cos x
\]

---

**Explanation:**
The boxes (\(\square\)) are placeholders for coefficients that result from applying trigonometric identities. Specifically, the task requires using sum and double angle formulas to express \(\cos 3x\) solely with powers of \(\cos x\). Calculating each step provides insight into the relationships between trigonometric functions.
Transcribed Image Text:**Transcription:** **Title: Using Trigonometric Identities** **Instructions:** Use the sum and double angle identities to write \(\cos 3x\) in terms of \(\cos x\): \[ \cos 3x = \square \cos^3 x + \square \cos^2 x + \square \cos x \] --- **Explanation:** The boxes (\(\square\)) are placeholders for coefficients that result from applying trigonometric identities. Specifically, the task requires using sum and double angle formulas to express \(\cos 3x\) solely with powers of \(\cos x\). Calculating each step provides insight into the relationships between trigonometric functions.
**Title: Using Sum and Double Angle Identities in Trigonometry**

---

**Explanation:**

In this exercise, we aim to express \( \cos 3x \) in terms of \( \cos x \) using sum and double angle identities. This involves recognizing patterns based on known trigonometric identities to simplify expressions.

**Equation Example:**

\[ \cos 3x = \_ \, \cos^3 x + \_ \, \cos^2 x + \_ \]

The blanks in the equation are editable fields where students can select from a dropdown menu of numbers ranging from \(-9\) to \(9\).

---

**Additional Exercise:**

Following this, students are instructed to express other trigonometric functions in terms of a given angle \( \theta \). 

**Tasks:**

- Write the trigonometric expression as a function of \( \theta \).

1. \( \cos(\theta + \_) \)
2. \( \cos(90^\circ - \theta) = \)
3. \( \cos(2\theta) = \)
4. \( \sin(\_) = \)

Students should fill in these expressions by applying their understanding of trigonometric identities.

---

**Study Tip:**

- Recall key identities like the angle addition formulas and triple angle formulas for efficient solving.
- Practice by filling the blanks with the correct numbers from the dropdown and comparing your results with established identities to ensure accuracy.
Transcribed Image Text:**Title: Using Sum and Double Angle Identities in Trigonometry** --- **Explanation:** In this exercise, we aim to express \( \cos 3x \) in terms of \( \cos x \) using sum and double angle identities. This involves recognizing patterns based on known trigonometric identities to simplify expressions. **Equation Example:** \[ \cos 3x = \_ \, \cos^3 x + \_ \, \cos^2 x + \_ \] The blanks in the equation are editable fields where students can select from a dropdown menu of numbers ranging from \(-9\) to \(9\). --- **Additional Exercise:** Following this, students are instructed to express other trigonometric functions in terms of a given angle \( \theta \). **Tasks:** - Write the trigonometric expression as a function of \( \theta \). 1. \( \cos(\theta + \_) \) 2. \( \cos(90^\circ - \theta) = \) 3. \( \cos(2\theta) = \) 4. \( \sin(\_) = \) Students should fill in these expressions by applying their understanding of trigonometric identities. --- **Study Tip:** - Recall key identities like the angle addition formulas and triple angle formulas for efficient solving. - Practice by filling the blanks with the correct numbers from the dropdown and comparing your results with established identities to ensure accuracy.
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