Exploring Sine, Cosine, and Tangent Function Values

In this lesson, the teacher explains the cosine and sine functions, focusing on solving for X and Y using these functions. The lesson covers angles and reference triangles, particularly multiples of pi/6 and pi/4, and provides example problems to illustrate the concepts. The teacher also demonstrates reverse calculations to find theta and radius from given coordinates. The lesson concludes with final examples and a reminder to memorize key angles and values.

What is the formula for cosine of theta as taught in the lesson?

• cos(theta) = r / y

• cos(theta) = x / r

• cos(theta) = r / x

• cos(theta) = y / r

If the radius (r) is 6 and theta is 5pi/6, what is the x-coordinate?

• 3 sqrt(3)

• -3 sqrt(3)

• -3

• 3

What is the y-coordinate when r = 6 and theta = 5pi/6?

• 6

• -3

• -6

• 3

For theta = pi/3 and r = 7, what is the x-coordinate?

• -7 sqrt(3) / 2

• 3.5

• 7 sqrt(3) / 2

• 7

Given the coordinates (-sqrt(2)/2, -sqrt(2)/2), what is the value of theta?

• 3pi/4

• 7pi/4

• 5pi/4

• pi/4

What is the radius if the coordinates are (-sqrt(2)/2, -sqrt(2)/2)?

• 2

• 1/2

• 1

• sqrt(2)

For the coordinates (-3 sqrt(3)/2, -3), what is the value of theta?

• 7pi/6

• pi/6

• 11pi/6

• 5pi/6

What is the radius if the coordinates are (-3 sqrt(3)/2, -3)?

• 3

• 6

• 4

• 2

If the coordinates are (-2, 2 sqrt(3)), what is the value of theta?

• pi/3

• 2pi/3

• 4pi/3

• 5pi/3

What is the radius for the coordinates (-2, 2 sqrt(3))?

• 8

• 2

• 4

• 6