Use the given information to find sin(s + t). See Example 3.
cos s = -1/5 and sin t = 3/5, s and t in quadrant II

Verified step by step guidance

1. Step 1: Use the Pythagorean identity to find sin(s).
2. Since \( \cos s = -\frac{1}{5} \), use \( \sin^2 s + \cos^2 s = 1 \) to find \( \sin s \).
3. Calculate \( \sin s = \sqrt{1 - \left(-\frac{1}{5}\right)^2} \).
4. Step 2: Determine the sign of \( \sin s \) based on the quadrant.
5. Since \( s \) is in quadrant II, \( \sin s \) is positive.

Key Concepts

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. One key identity is the sine addition formula, which states that sin(s + t) = sin(s)cos(t) + cos(s)sin(t). Understanding these identities is crucial for solving problems involving the sum of angles.

Quadrants and Signs of Trigonometric Functions

The unit circle is divided into four quadrants, each affecting the signs of the trigonometric functions. In quadrant II, sine is positive while cosine is negative. Knowing the quadrant in which angles s and t lie helps determine the signs of sin(s) and cos(s), which is essential for accurately calculating sin(s + t).

Pythagorean Theorem in Trigonometry

The Pythagorean theorem relates the sides of a right triangle and is fundamental in trigonometry. For any angle, the relationship sin²(θ) + cos²(θ) = 1 holds true. This theorem allows us to find missing trigonometric values, such as cos(s) when sin(s) is known, by using the known values and the relationship between sine and cosine.