# Know and use tanθ = sinθ / cosθ = and sin^2 θ + cos^2 θ = 1

## Know and use tanθ = sinθ / cosθ = and sin^2 θ + cos^2 θ = 1

# Understanding the Trig Identity tanθ = sinθ / cosθ

**tanθ**is the ratio of sine to cosine, expressed as**tanθ = sinθ / cosθ**.- Remember, each trigonometric function represents a ratio of sides in a triangle, specifically:
**sinθ**is the ratio of*opposite/hypotenuse*,**cosθ**is the ratio of*adjacent/hypotenuse*, and**tanθ**is the ratio of*opposite/adjacent*.

# Using tanθ = sinθ / cosθ

**tanθ**is used in right-angled triangles when you have the measures of the opposite and adjacent sides but not the hypotenuse.- The expression
**tanθ = sinθ / cosθ**can be used as another method to find angles or length of sides in a triangle. - This ratio can also be useful for solving problems in the Cartesian coordinate system where x (cosθ) and y (sinθ) coordinates are used.

# Understanding the Pythagorean Identity sin²θ + cos²θ = 1

- Known as the
**Pythagorean trigonometric identity**. This identity reveals a direct relationship between the sine and cosine functions. - The identity
**sin²θ + cos²θ = 1**holds true for any real number θ.

# Using the Pythagorean Identity sin²θ + cos²θ = 1

- This identity is useful in proving other identities or simplifying trigonometric expressions.
- It can help find missing side lengths in right angle triangles when only one side and one angle is known.
- It’s even used outside trigonometry, like in calculus for integrals or derivatives involving sine and cosine.
- Moving parts of the identity around allows you to find sine from cosine and vice-versa, by using
**sin²θ = 1 - cos²θ**or**cos²θ = 1 - sin²θ**respectively.