4d Example 2 (Evaluating trig functions with the same reference angle)

The video tutorial explores the evaluation of trigonometric functions using the unit circle. It begins with an introduction to angles intersecting the unit circle and special right triangles. The instructor demonstrates how to evaluate the sine of π/3 and 4π/3, highlighting the concept of reflections and reference angles. The tutorial continues with the evaluation of sine for 5π/6, emphasizing the use of reference angles and quadrant analysis. Finally, the tangent of π/4 and its negative counterpart are discussed, showcasing the importance of understanding reference angles and quadrant signs for efficient trigonometric evaluation.

What is the sine of π/3 based on the unit circle?

• 1/2

• sqrt(3)/2

• -sqrt(3)/2

• sqrt(2)/2

How does the angle 4π/3 relate to the unit circle?

• It is not a reflection.

• It is a reflection about the origin.

• It is a reflection about the y-axis.

• It is a reflection about the x-axis.

What is the reference angle for 4π/3?

• π/4

• π/2

• π/3

• π/6

What is the cosine of 5π/6?

• -sqrt(3)/2

• 1/2

• -1/2

• sqrt(3)/2

How does the reference angle help in evaluating trigonometric functions?

• It helps identify the quadrant of the angle.

• It determines the exact value of the function.

• It is not useful in trigonometry.

• It simplifies the calculation by using known values from the first quadrant.

What is the tangent of π/4?

• sqrt(2)/2

• 1

• -1

• 0

Why is the tangent of -π/4 negative?

• Because it is in the fourth quadrant.

• Because it is in the third quadrant.

• Because it is in the second quadrant.

• Because it is in the first quadrant.