Reference Triangles and Trigonometric Functions

The video tutorial introduces trigonometry on the unit circle, focusing on special angles and their coordinates. It then transitions to reference triangles, which allow trigonometric calculations for points not on the unit circle. The tutorial explains how to use similar triangles to express trigonometric functions in terms of known coordinates and calculates the hypotenuse using the Pythagorean theorem. The video concludes with a summary and a preview of upcoming examples.

What is the x-coordinate of the cosine of π/6 on the unit circle?

• 1/2

• √3/2

• 0

• 1

What is the y-coordinate of the sine of π/6 on the unit circle?

• 0

• 1/2

• √3/2

• 1

What happens if a point is not on the unit circle?

• We use reference triangles

• We ignore the point

• We use a different circle

• We cannot use trigonometric functions

What is a reference triangle?

• A triangle with no right angle

• A triangle with all sides equal

• A triangle used to calculate angles

• A triangle used to express trig functions for points not on the unit circle

In a reference triangle, what do we call the known point?

• p, q

• x, y

• a, b

• m, n

How do we express cosine of θ using a reference triangle?

• Adjacent over opposite

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Hypotenuse over adjacent

What is the formula for the hypotenuse in a reference triangle?

• r = √(x^2 + y^2)

• r = x^2 + y^2

• r = x + y

• r = x/y

What is the purpose of using reference triangles?

• To express trig functions for points off the unit circle

• To simplify calculations

• To find the area of a triangle

• To avoid using the unit circle