Learn: Trigonometric Ratios

Welcome!Today we'll explore trigonometric ratios, a key topic in iGCSE Mathematics. These ratios help us solve problems involving angles and sides in right-angled triangles. Let's break it down step by step!

What are Trigonometric Ratios?Trigonometric ratios relate the angles and sides of a right-angled triangle. The three main ratios are sine (sin), cosine (cos), and tangent (tan). They are used to calculate unknown side lengths or angles.

Main RatiosThe definitions of the ratios are:Sine: sin(angle) = opposite / hypotenuseCosine: cos(angle) = adjacent / hypotenuseTangent: tan(angle) = opposite / adjacentThese ratios depend on the position of the angle in the triangle.

Using Trigonometric RatiosTo use trigonometric ratios effectively, you must identify the correct sides relative to the angle:Opposite: The side directly opposite the angle.Adjacent: The side next to the angle, but not the hypotenuse.Hypotenuse: The longest side in the triangle, opposite the right angle.Once identified, apply the correct ratio formula.

Exact Values for Common AnglesFor special angles like 0°, 30°, 45°, 60°, and 90°, the trigonometric ratios have exact values:sin(30°) = 1/2cos(45°) = √2/2tan(60°) = √3These values are often used in exam questions and must be remembered.

Finding UnknownsTo find an unknown side or angle in a right-angled triangle:Identify the sides relative to the angle (opposite, adjacent, hypotenuse).Choose the correct ratio (sin, cos, or tan).Rearrange the formula to solve for the unknown.Use a calculator if needed.Example: To find the hypotenuse when opposite = 4 and angle = 30°, use sin(30°) = 4 ÷ hypotenuse.

Review Time!Great work! You've learned about trigonometric ratios, their definitions, and how to use them to solve problems. Let's test your understanding with a few final questions.