Pre-Calculus: Trigonometry Basics: Challenge

# Hard Level Guide Stretch thinking with multi-step problems, application questions, and deeper reasoning. # Right Triangle Ratios For angle θ in a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. SOH-CAH-TOA helps remember. Use a calculator for non-special angles in degrees or radians. # Special Right Triangles A 45-45-90 triangle has legs 1 and hypotenuse √2. A 30-60-90 triangle has sides 1, √3, and 2. These exact values appear on the unit circle and simplify many problems without a calculator. # The Unit Circle A circle with radius 1 centered at the origin. Each point (x, y) on the circle gives cos θ = x and sin θ = y for angle θ in standard position. Quadrant signs follow ASTC (All Students Take Calculus) mnemonic. # Radians and Applications π radians equals 180 degrees. Arc length and angular speed use radians. Trigonometry models periodic phenomena like sound waves and seasons. Inverse trig functions find angles from ratios.