Trigonometry- Sin, Cos and Tan

Trigonometry: Sin, Cos, and Tan

Understanding Trigonometry

Trigonometry is a key branch of maths dealing with the relationships among sides and angles in triangles.
Derived from Greek, trigonometry means ‘measurement of three angles’.
In everyday applications, trigonometry is used in fields like engineering, physics, and computer graphics.

Key Trigonometric Ratios

The central concept in trigonometry is the use of ratios to represent relationships among sides of a triangle.
There are three primary trigonometric ratios: sine (sin), cosine (cos), and tangent (tan).

The Sine (sin) Function

In a right-angled triangle, the sine of an angle is the ratio of the length of the side opposite that angle to the length of the hypotenuse.
For an angle θ, this could be written as sin θ = opposite/hypotenuse.

The Cosine (cos) Function

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.
You can express this as cos θ = adjacent/hypotenuse.

The Tangent (tan) Function

The tangent of an angle is the ratio of the opposite side to the adjacent side.
Typically, this rule is written as tan θ = opposite/adjacent.
Noticeably, tan θ can also be expressed as tan θ = sin θ/cos θ.

Using Sin, Cos, and Tan

Remembering the definitions of sin, cos, and tan can be made easier with the acronym SOHCAHTOA, which stands for ‘Sine is Opposite over Hypotenuse, Cosine is Adjacent over Hypotenuse, Tangent is Opposite over Adjacent’.
These functions play an integral role in calculating distances or angles in a right-angled triangle and perform transformations and rotations in geometry.
When given any two sides of a right-angled triangle, you can calculate any angle using the appropriate function and inverse (sin⁻¹, cos⁻¹, or tan⁻¹), depending on what data you have.

Applying Trigonometric Functions

Calculators typically include built-in functionality for sin, cos, and tan, which will be essential for tackling more complex problems.
Regular practice with different types of triangles will strengthen your understanding of when and how to use these functions accurately,
You can apply the concepts behind sin, cos, and tan beyond simple triangle problems. They have diverse applications in most forms of pure and applied maths.

Understanding and mastering sin, cos, and tan is not only crucial for solving triangle problems, it also forms the foundation for more advanced mathematical concepts. As you become comfortable with these fundamental trigonometric functions, you’ll find that they unlock a wealth of possibilities in your mathematical explorations.