Trigonometric functions like sine, cosine, and tangent are really important for figuring out how the angles and sides of right triangles work together.

What They Mean:

1. Sine (sin): For an angle called $\theta$, the sine function shows the relationship between the length of the side opposite the angle and the length of the longest side (the hypotenuse). We write it like this: $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$

2. Cosine (cos): The cosine function compares the length of the side next to the angle (the adjacent side) to the length of the hypotenuse. It looks like this: $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$

3. Tangent (tan): The tangent function is about comparing the opposite side to the adjacent side. It can be written as: $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$

How They Relate:

• The sine and cosine functions work together with the tangent in this equation: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$

• These tools are very helpful when solving problems involving right triangles.

Other Functions:

There are also three more trigonometric functions that relate back to sine, cosine, and tangent:

1. Cosecant (csc): $\csc(\theta) = \frac{1}{\sin(\theta)} = \frac{\text{Hypotenuse}}{\text{Opposite}}$

2. Secant (sec): $\sec(\theta) = \frac{1}{\cos(\theta)} = \frac{\text{Hypotenuse}}{\text{Adjacent}}$

3. Cotangent (cot): $\cot(\theta) = \frac{1}{\tan(\theta)} = \frac{\text{Adjacent}}{\text{Opposite}}$

Where They Are Used:

Trigonometric functions are used a lot in areas like physics, engineering, and architecture. They help us measure distances, angles, and describe things that happen in cycles. Learning about these functions is an important part of the Grade 12 Pre-Calculus course.