Use reference angles to find the exact value of the expression.
cot(315°)

To find the exact value of \(\cot(315^\circ)\) using reference angles, follow these steps:

### Step 1: Find the reference angle
The given angle is \(315^\circ\), which is in the fourth quadrant. The reference angle is the positive acute angle formed with the x-axis. 

To calculate the reference angle, subtract \(315^\circ\) from \(360^\circ\):
\[
360^\circ - 315^\circ = 45^\circ
\]
So, the reference angle is \(45^\circ\).

### Step 2: Determine the cotangent of the reference angle
The cotangent of \(45^\circ\) is known:
\[
\cot(45^\circ) = 1
\]

### Step 3: Determine the sign of \(\cot(315^\circ)\)
In the fourth quadrant, the cotangent function is negative. Therefore:
\[
\cot(315^\circ) = -\cot(45^\circ) = -1
\]

### Final Answer:
\[
\cot(315^\circ) = -1
\]

Would you like further explanation on any step?

---

Here are 5 related questions:
1. What is the reference angle for \(225^\circ\)?
2. How do you find the exact value of \(\cot(120^\circ)\)?
3. What is the value of \(\cot(30^\circ)\)?
4. How do you find the reference angle for angles greater than \(360^\circ\)?
5. What is the difference between cotangent and tangent?

**Tip:** Cotangent is the reciprocal of tangent. If \(\tan(\theta) = x\), then \(\cot(\theta) = \frac{1}{x}\).

Use reference angles to find the exact value of the expression. cot(315°)

Learn how to find the exact value of cot(315°) using reference angles. This step-by-step solution explores key trigonometric concepts, including the cotangent function, reference angles, and the behavior of trigonometric functions in the fourth quadrant. Perfect for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation