Use the identity cos²s + sin²s =1 to find the value of (⅗,y),y is greater than 0

We are given that \( \cos s = \frac{3}{5} \) and we need to find the value of \( y \), where \( y = \sin s \), using the Pythagorean identity:

\[
\cos^2 s + \sin^2 s = 1
\]

Substitute \( \cos s = \frac{3}{5} \) into the equation:

\[
\left( \frac{3}{5} \right)^2 + \sin^2 s = 1
\]

\[
\frac{9}{25} + \sin^2 s = 1
\]

Subtract \( \frac{9}{25} \) from both sides:

\[
\sin^2 s = 1 - \frac{9}{25}
\]

To find a common denominator on the right side:

\[
\sin^2 s = \frac{25}{25} - \frac{9}{25} = \frac{16}{25}
\]

Now, take the square root of both sides:

\[
\sin s = \pm \frac{4}{5}
\]

Since \( y = \sin s \) and \( y \) is given to be greater than 0, we choose the positive root:

\[
y = \frac{4}{5}
\]

Thus, the value of \( y \) is \( \frac{4}{5} \).

Would you like further details or explanations?

Here are five related questions:
1. How can this identity be used for other angles?
2. What are the values of \( \cos s \) and \( \sin s \) if \( \sin s \) was less than 0?
3. How can we verify this solution using a right triangle?
4. What are the values of \( \tan s \) and \( \sec s \) for this angle?
5. How does this identity help in trigonometric simplifications?

**Tip:** The Pythagorean identity is one of the most important in trigonometry, useful for converting between sine and cosine values easily.

Use the identity cos²s + sin²s =1 to find the value of (⅗,y), y is greater than 0

Learn how to use the Pythagorean identity cos²s + sin²s = 1 to find the sine value when cos(s) = 3/5. Follow this step-by-step solution to calculate sin(s) when y is greater than 0. Ideal for students in Grades 9-11 studying trigonometry.

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