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.

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.

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.

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.