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Trigonometry: FAQ

Frequently asked questions about trigonometry

What is the unit circle and why is it important in trigonometry?

The unit circle is a circle with a radius of 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- and y-coordinates of a point moving around the circle.

What are radians and why do we use them in trigonometry?

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.
A circle. There are two radii that form a central angle. The arc length is shown to be equal to the length of the radius.
We often use radians in trigonometry because they make working with trigonometric functions easier.

What is the Pythagorean identity and why is it important?

The Pythagorean identity is 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.

What do amplitude, midline, and period mean when we're talking about sinusoidal graphs?

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.

Why do we want to know how to transform sinusoidal graphs?

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.

Where are trigonometric functions used in the real world?

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.

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