Exploring Sin, Cos, and Tan on the Unit Circle

The video tutorial covers solving trigonometric problems using the unit circle. It begins with three problems: cosine of negative 90 degrees, sine of five pi over two, and tangent of 300 degrees. The instructor explains each problem step-by-step, using the unit circle to find the solutions. The video concludes with an example involving non-traditional coordinates, demonstrating how to calculate the tangent of an angle using given coordinates. The tutorial emphasizes understanding the unit circle and converting angles between degrees and radians.

What is the cosine of -90 degrees?

• 1

• -1

• undefined

• 0

How do you adjust the angle -90 degrees to find its cosine using the unit circle?

• No adjustment needed

• Add 180 degrees

• Subtract 90 degrees

• Add 360 degrees

What is the sine of 5 PI/2?

• 0

• -1

• 1

• undefined

How is 5 PI/2 converted to a standard position on the unit circle?

• Subtract PI

• Add 2 PI

• Subtract 2 PI

• No conversion needed

What is the tangent of 300 degrees?

• -sqrt(3)

• sqrt(3)

• 0

• 1

How do you calculate the tangent of an angle using the unit circle?

• Divide the y-coordinate by the x-coordinate

• Multiply the x-coordinate by the y-coordinate

• Subtract the y-coordinate from the x-coordinate

• Add the x-coordinate to the y-coordinate

What is the tangent of an angle with coordinates (2/3, -sqrt(5)/3)?

• 2/3

• sqrt(5)/2

• -sqrt(5)/2

• -2/3

In which quadrant does the coordinate (2/3, -sqrt(5)/3) lie?

• Quadrant I

• Quadrant III

• Quadrant IV

• Quadrant II

What is the process to find the degree measure of an angle if you know the tangent value?

• Multiply by 180/PI

• Use the cosine function

• Use the sine function

• Use the inverse tangent function

What is the result of adding 360 degrees to a negative angle measure in the context of the unit circle?

• Inverts the angle

• Changes the angle to zero

• No change to the angle

• Converts it to a positive standard position