Trigonometric Functions and Reference Triangles

The video tutorial explains how to use reference triangles to evaluate trigonometric functions. It begins with an introduction to reference triangles and sets up an example using a point not on the unit circle. The tutorial verifies the point's position relative to the unit circle, constructs a reference triangle, and calculates the trigonometric functions. It concludes with finding reciprocal trigonometric functions, emphasizing the importance of understanding the triangle's geometry.

What is the first step in solving the problem with reference triangles?

• Plotting the point on the graph

• Calculating the hypotenuse

• Verifying if the point is on the unit circle

• Evaluating trigonometric functions

What does it mean for an angle to be in standard position?

• Vertex at the origin, initial side on the negative x-axis

• Vertex at the point, initial side on the negative y-axis

• Vertex at the point, initial side on the y-axis

• Vertex at the origin, initial side on the positive x-axis

How do you verify if a point is on the unit circle?

• Check if the point lies in the first quadrant

• Check if the x-coordinate is greater than the y-coordinate

• Check if the coordinates are both positive

• Check if the sum of the squares of the coordinates equals 1

What is the significance of the point (2, 3) in this problem?

• It is the point through which the terminal side of the angle passes

• It is the vertex of the angle

• It is the midpoint of the hypotenuse

• It is the endpoint of the initial side

How is the hypotenuse of the reference triangle calculated?

• Using the distance formula

• Using the Pythagorean theorem

• By adding the x and y coordinates

• By measuring directly on the graph

What is the cosine of theta in this example?

• 3 over 2

• 3 over root 13

• 2 over root 13

• 2 over 3

What is the sine of theta in this example?

• 3 over 2

• 2 over 3

• 3 over root 13

• 2 over root 13

What is the tangent of theta in this example?

• 2 over 3

• 3 over root 13

• 2 over root 13

• 3 over 2

What is the secant of theta in this example?

• Root 13 over 2

• 2 over root 13

• 3 over root 13

• Root 13 over 3

What is the cosecant of theta in this example?

• Root 13 over 2

• 2 over root 13

• Root 13 over 3

• 3 over root 13