Trigonometry: FAQ

The unit circle is a circle with a radius of $1$1 that is centered at the origin on a coordinate plane. It's important in trigonometry because it allows us to define the sine and cosine functions in terms of the $x$x- and $y$y-coordinates of a point moving around the circle.

Radians are a unit of measurement for angles.

One radian is the angle measure that we turn to travel one radius length around the circumference of a circle.

We often use radians in trigonometry because they make working with trigonometric functions easier.

The Pythagorean identity is $\sin^2x+\cos^2x=1$sine, squared, x, plus, cosine, squared, x, equals, 1. It comes from the Pythagorean theorem and is important in trigonometry because it can help us solve for the value of one trigonometric function if we know the other.

The amplitude of a sinusoidal graph is the distance from the midline to the highest or lowest point on the graph. The midline is the horizontal line that the graph oscillates around, and the period is the horizontal distance it takes for the graph to complete one full cycle.

By understanding how to transform sinusoidal graphs, we can graph a wider variety of sinusoidal functions. For example, we can change the amplitude, midline, or period to match a given equation.

Trigonometric functions are used in many real-world applications. For example, engineers use them to design bridges, and physicists use them to model periodic phenomena such as waves or vibrations.