if x=costheta then was is sintheta in terms of x?

Given that \( x = \cos(\theta) \), we want to express \( \sin(\theta) \) in terms of \( x \).

We can use the Pythagorean identity:

\[
\sin^2(\theta) + \cos^2(\theta) = 1
\]

Substituting \( \cos(\theta) = x \) into the identity:

\[
\sin^2(\theta) + x^2 = 1
\]

Now, solve for \( \sin^2(\theta) \):

\[
\sin^2(\theta) = 1 - x^2
\]

Taking the square root of both sides:

\[
\sin(\theta) = \pm \sqrt{1 - x^2}
\]

Therefore, \( \sin(\theta) \) in terms of \( x \) is:

\[
\sin(\theta) = \pm \sqrt{1 - x^2}
\]

The \( \pm \) sign depends on the quadrant in which the angle \( \theta \) is located.

Would you like further details or have any questions?

Here are 5 related questions you might consider:
1. What is \( \tan(\theta) \) in terms of \( x \)?
2. How do you determine the correct sign for \( \sin(\theta) \)?
3. What is \( \sin(2\theta) \) in terms of \( x \)?
4. Can you express \( \theta \) in terms of \( x \)?
5. How would you solve for \( \theta \) given a specific value of \( x \)?

**Tip:** Remember that the sign of \( \sin(\theta) \) depends on the angle's quadrant in the unit circle.

Learn how to express sin(theta) in terms of cos(theta) = x using the Pythagorean identity. Detailed step-by-step solution provided, covering trigonometric concepts and identities. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation