Find the exact value of tangent, start fraction, pi, divided by, 4, end fractiontan 
4
π
​
 , expressing your answer with a rational denominator.

To find the exact value of \(\tan\left(\frac{\pi}{4}\right)\), we can follow these steps:

1. We know that \(\frac{\pi}{4}\) radians is equivalent to 45 degrees.

2. The tangent of 45 degrees is known to be 1, as \(\tan(45^\circ) = 1\).

Thus, \(\tan\left(\frac{\pi}{4}\right) = 1\).

Since 1 is already a rational number, the exact value of \(\tan\left(\frac{\pi}{4}\right)\) is:

\[
\tan\left(\frac{\pi}{4}\right) = 1
\]

Would you like more details on trigonometric values or have any questions?

Here are five related questions:
1. What is the exact value of \(\sin\left(\frac{\pi}{4}\right)\)?
2. What is the value of \(\tan\left(\frac{3\pi}{4}\right)\)?
3. Can you calculate \(\tan(30^\circ)\) in exact form?
4. How would you convert radians to degrees?
5. What is the exact value of \(\sec\left(\frac{\pi}{3}\right)\)?

**Tip:** Tangent is the ratio of sine to cosine: \(\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\). This relationship helps in finding its value in various angles.

Find the exact value of tangent, start fraction, pi, divided by, 4, end fraction, expressing your answer with a rational denominator.

Find the exact value of tan(π/4) using trigonometric principles. This detailed explanation shows how the tangent of 45 degrees, or π/4 radians, equals 1, with a focus on rational denominators. Ideal 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