Essential Trigonometric Formulas

Ever wondered how to find missing sides or angles in a triangle? Trigonometric ratios are your answer! Remember SOH-CAH-TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent. Their reciprocals are cosecant, secant, and cotangent respectively.

Converting between degrees and radians is simple: multiply degrees by π/180° to get radians, or multiply radians by 180°/π to get degrees. For arc length, use s = rθ where r is radius and θ is in radians.

The Pythagorean identities connect trig functions: sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, and 1 + cot²θ = csc²θ. These are super useful for simplifying expressions!

Pro Tip: When solving trigonometric problems, drawing a reference triangle can help you visualize which ratios to use. Label the hypotenuse, opposite, and adjacent sides relative to your angle.

Quotient identities show relationships between functions: tanθ = sinθ/cosθ and cotθ = cosθ/sinθ. For angles in standard position, use polar equations: x = rcosθ, y = rsinθ, and r² = x² + y².

The special angles chart (0°, 30°, 45°, 60°, 90°) gives you exact values without a calculator. Remember that reference angles help you find trig values in different quadrants, and even/odd identities tell you how functions behave with negative angles.