Learn: Trigonometry Basics

Welcome!Today, we'll explore the basics of Trigonometry. This is a key topic in iGCSE Mathematics that helps you solve problems involving angles and lengths in triangles. Let's dive in!

What is Trigonometry?Trigonometry is the study of the relationships between angles and sides in triangles, particularly right-angled triangles. It helps us calculate unknown angles or lengths, which is useful in many real-world applications like architecture, engineering, and navigation.

Key Trigonometric RatiosIn a right-angled triangle, there are three key trigonometric ratios to know:Sine (sin): Ratio of the length of the opposite side to the hypotenuse.Cosine (cos): Ratio of the length of the adjacent side to the hypotenuse.Tangent (tan): Ratio of the length of the opposite side to the adjacent side.

Using SOHCAHTOASOHCAHTOA is a handy way to remember the three trigonometric ratios:SOH: Sine = Opposite / HypotenuseCAH: Cosine = Adjacent / HypotenuseTOA: Tangent = Opposite / AdjacentIt's a mnemonic to help you select the correct ratio based on the sides and angles given in a right-angled triangle.

Pythagoras’ TheoremPythagoras’ theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This is written as a² + b² = c², where c is the hypotenuse.

Exact Trigonometric ValuesFor certain angles, the trigonometric ratios have exact values:sin: sin(30°) = 1/2, sin(45°) = √2/2, sin(60°) = √3/2cos: cos(30°) = √3/2, cos(45°) = √2/2, cos(60°) = 1/2tan: tan(30°) = √3/3, tan(45°) = 1, tan(60°) = √3

Review Time!Great work! You've learned about the basics of trigonometric ratios, Pythagoras' theorem, and exact values for special angles. Let's review everything you've covered.