Trigonometry – Right-Angled Triangles - Introduction to trigonometry
Trigonometry – Right-Angled Triangles - Introduction to trigonometry
Intro to Trigonometry
- Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles.
- It’s especially relevant to right-angled triangles, those with one angle equal to 90 degrees.
- The three main functions in trigonometry are sine (sin), cosine (cos), and tangent (tan).
- To remember these functions and their relationships, the acronym SOHCAHTOA is often used, which stands for Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, Tangent = Opposite / Adjacent.
- The ‘opposite’ is the side opposite the angle in question, the ‘adjacent’ is the side next to the angle, and the ‘hypotenuse’ is the longest side, always opposite the right angle.
Sine, Cosine, And Tangent
- The sine function (sin) of an angle in a triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
- The cosine function (cos) of an angle is the ratio of the length of the adjacent side to the hypotenuse.
- The tangent function (tan) of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
Practical Application
- Trigonometry is vital in physics, engineering, and computer programming, among other fields.
- In everyday life, it’s used for tasks like calculating distances, understanding waves (like sound or light), or in any situation where you need to relate the sides and angles of triangles.
For revision, practice the above concepts using examples of right-angled triangles. Discuss where the ‘opposite’, ‘adjacent’, and ‘hypotenuse’ are in relation to different right-angled triangles, and also practice calculating sine, cosine, and tangent values for different angles.