What are trigonometric functions and how are they used?

What are trigonometric functions and how are they used?

Trigonometric functions are mathematical functions that relate the angles of a triangle to the lengths of its sides. They are primarily used in geometry, physics, engineering, and many fields involving periodic phenomena.

Can you explain the main trigonometric functions?

Sure! The main trigonometric functions are sine (sin), cosine (cos), and tangent (tan). They are defined as follows:

• Sin(θ) = opposite side / hypotenuse
• Cos(θ) = adjacent side / hypotenuse
• Tan(θ) = opposite side / adjacent side.

How do these functions apply in real life?

Trigonometric functions are used in various real-life applications, such as calculating heights and distances, in navigation, in waves and oscillations, and in computer graphics to model periodic behavior.

What is the unit circle and how does it relate to trigonometric functions?

The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It helps define the trigonometric functions for all angles, as the coordinates of points on the circle correspond to the values of sine and cosine.

Can you give me an example of a problem involving trigonometric functions?

Absolutely! For example, if you want to find the height of a tree, you can measure the distance from the tree and the angle of elevation to the top. Using the tangent function, you can calculate the height using the formula: height = distance * tan(angle).