Trigonometry

Trigonometry

Basic Concepts

• Sine (sin), Cosine (cos), and Tangent (tan) are the primary functions in trigonometry. They are ratios of sides in a right-angled triangle.
• Reciprocal functions such as cosec, sec, and cot are also important to understand. They are the reciprocals of sin, cos, and tan respectively.
• The unit circle is a crucial concept. It helps to understand the trigonometric functions and their graphs.

Trigonometric Ratios

• Remember that for any given angle in a right angled triangle, sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side.
• These ratios remain constant no matter the size of the triangle.

Trigonometric Identities

• The Pythagorean identities are fundamental. The most basic one is sin²θ + cos²θ = 1.
• The double-angle and half-angle identities are also commonly used in further mathematics.

Solving Trigonometric Equations

• When solving trigonometric equations, it’s important to remember to check all quadrants for possible solutions.
• For simple equations, the unit circle can be used to directly find the solution. For more complicated equations, it’s often necessary to use trigonometric identities.

Graphs of Trigonometric Functions

• Understanding how the graphs of the functions sin, cos, and tan behave is very important. Remember that sin and cos are periodic with period 2π, while tan has a period of π.