# 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.