Learn: Trigonometry Basics

Welcome!Today we’ll explore trigonometry, focusing on its basics and why it’s useful in solving right-angled triangle problems. Let’s get started!

What is Trigonometry?Trigonometry is the study of the relationships between angles and sides in triangles. Specifically, it is most commonly applied to right-angled triangles. It helps us calculate missing angles or side lengths when certain information is provided.

Key Trigonometric RatiosThere are three main trigonometric ratios:Sine (sin) — This is the ratio of the opposite side to the hypotenuse.Cosine (cos) — This is the ratio of the adjacent side to the hypotenuse.Tangent (tan) — This is the ratio of the opposite side to the adjacent side.We use these ratios to solve for unknown angles or sides in right-angled triangles.

How to use Trigonometric RatiosTo use trigonometric ratios, follow these steps:Identify the given angle in the triangle.Label the sides as opposite, adjacent, and hypotenuse based on the angle.Select the appropriate ratio based on the sides you know and what you need to find (sin, cos, or tan).Substitute the values into the formula and solve.

Remember SOHCAHTOA!The mnemonic SOHCAHTOA helps you remember the trigonometric ratios:SOH: Sine = Opposite / HypotenuseCAH: Cosine = Adjacent / HypotenuseTOA: Tangent = Opposite / Adjacent

Exact Values of Special AnglesSome angles have exact trigonometric values that you should memorise:sin(30°) = 1/2cos(30°) = √3/2tan(45°) = 1sin(90°) = 1These values are often used in calculations involving triangles.

Using Inverse Trigonometric RatiosWe use inverse trigonometric functions to find angles when the sides are known:sin⁻¹, cos⁻¹, and tan⁻¹ are used for this purpose.For example, if you know the opposite side and hypotenuse, you can use sin⁻¹(opposite/hypotenuse) to calculate the angle.

Solving Trigonometry ProblemsLet’s try solving a problem. Imagine a ladder leaning against a wall forms a right-angled triangle with the ground. The ladder is 5 m long, and the distance between the bottom of the ladder and the wall is 3 m. What is the angle between the ladder and the ground?

Review Time!Great work! You've learned about trigonometric ratios, SOHCAHTOA, and solving problems using trigonometry. Let’s review what you’ve learned.