Sine

5.3 Solution of Trigonometric Equations

Basic Trigonometric Equations (Sine and Cosine)

The most basic equations in polynomials would be linear equations, such as $ax+b=c$ (which gives you $x=\frac{c-b}{a}$ ). The trigonometric equivalent ones would be $\sin t =a$ or $\cos t =b$ , and you are supposed to solve for $t$ .

Be careful, as solving trigonometric equations are not as simple. Refer to the examples below.

For each such equations, unless a restriction on $x$ (or more commonly used in trigonometric, $\theta$ ), there will be infinite or no solutions for $x$ . This is because of the periodic and symmetric properties that they have.

Degrees and Radians

All these while we are familiar with degrees. We know that a straight line is $180^{\circ}$ , and for a full circle it is $360^{\circ}$ .
There is another unit to represent degrees, it is known as radians.
The short form of radians can be written in several ways. Take 1 radian for example. The most formal way would be written as $1^{c}$ . It can be written as $1\ \mathrm{rad}$ as before, or the most common way, $1$ (without any units).
The term ‘radian’ actually originated when we wanted to find a neat expression for the angle when the corresponding arc length of a circle with 1 unit radius, for this angle, is also 1 unit. Using degrees, the number will not look nice, hence a new unit called radians are invented.
Radians are useful as it can be treated as numbers (without units).
Radians are defined as positive for angles moving anticlockwise. For the diagram at the right, that is a positive angle (1 rad). It is similar to how we define $90^{\circ}$ and $-90^{\circ}$ .
The conversion from radian to degrees is:

Derivatives [Video Tutorial]

This tutorial covers material encountered in chapter 9 of the VCE Mathematical Methods Textbook, namely: The derivative of functions seen previously in tutorial worksheets 1-5… Read More »Derivatives [Video Tutorial]

Trigonometric functions [Video Tutorial]

This tutorial covers material encountered in chapter 6 of the VCE Mathematical Methods Textbook, namely: Radians The sine, cosine and tangent functions The unit circle… Read More »Trigonometric functions [Video Tutorial]