# Basics of Trigonometry in Triangles

• The key to understanding trigonometry in triangles is sin, cos, and tan. These are ratios defined for any angle, they represent the ratios of different possible pairings of the sides in a right triangle.

• In any right triangle, sin (theta) equals the length of the opposite side (O) divided by the length of the hypotenuse (H).

• The abbreviation SOH helps to remember this as Sine = Opposite/Hypotenuse.

# Cosine Rule

• Cos (theta) equals the length of the adjacent side (A) divided by the length of the hypotenuse (H).

• The abbreviation CAH helps to remember this as Cosine = Adjacent/Hypotenuse.

# Tangent Rule

• Tan (theta) equals the length of the opposite side (O) divided by the length of the adjacent side (A).

• The abbreviation TOA helps remember this as Tangent = Opposite/Adjacent.

# Pythagorean Relationship

• Sin²(theta) + Cos²(theta) = 1 is called the Pythagorean Trig Identity. This formula shows the relationship between sin, cos, and tan.

# Trigonometry in Non-Right Triangles

• The Law of Sines can be used to find missing side lengths and angles in any triangle, not just right triangles.

• The Law of Cosines is useful for finding a triangle’s angles when we know all three sides.

# Inverse Trigonometric Functions

• The inverse trigonometric functions sin⁻¹, cos⁻¹, and tan⁻¹ are used to find the angle when we know the ratio of the sides in a right triangle.