Unit Circle Applications

Evaluate sine of 45॰ using the unit circle and right triangle trigonometry. What is the connection between the y coordinate of the point and the sine of the angle?

• sqrt(2)/2, the sine of 45 degrees is the y value of the ordered pair at 45 degrees

• sqrt(2)/2, the sine of 45 degrees is the x value of the ordered pair at 45 degrees

• 1/2, the sine of 45 degrees is the y value of the ordered pair at 45 degrees

• 1/2, the sine of 45 degrees is the x value of the ordered pair at 45 degrees

Tags

CCSS.HSF.TF.A.2

If the tide height at a marina is modeled by 𝑦 = 2𝑐𝑜𝑠(𝑡) -1 with 𝑦 measured in feet and 𝑡 measured in hours, find 𝑡 if the height is 1 foot. Express your answers in terms of the unit circle ( degrees )

• 90 and 270

• 0

• 180

• 90 and 45

Tags

CCSS.HSF.TF.B.7

Evaluate tangent of 270॰ using the unit circle and right triangle trigonometry. What is the connection between the x and y coordinates and the tangent of the angle.

• sqrt(3)/3, the tangent of 270 degrees is the y value divided by the x value of the ordered pair at 270 degrees

• sqrt(3), the tangent of 270 degrees is the y value divided by the x value of the ordered pair at 270 degrees

• 0, the tangent of 270 degrees is the y value of the ordered pair at 270 degrees

• Undefined, the tangent of 270 degrees is the y value divided by the x value of the ordered pair at 270 degrees

Tags

CCSS.HSF.TF.A.2

A child enters a carousel that takes one minute to revolve once around. The child enters at the point (0,1) that is, on the due north position. Assume the carousel revolves counter clockwise. At what position would the child be after 180 seconds.

• (-1,0)

• (sqrt2/2, sqrt2/2)

• (sqrt3/2, 1/2)

• (0, -1)

Tags

CCSS.HSF.TF.B.7

The speed of a sound wave is modeled by the equation 𝑦 = 10sin(𝑡) -2 with 𝑦 measured in meters and 𝑡 measured in seconds, how long did it take for the sound wave to travel 3 meters? . Express your answers in terms of the unit circle ( degrees )

• 30 and 150

• 240 and 315

• 30 and 60

• 30 and 210

Tags

CCSS.HSF.TF.B.7

The horizontal distance 𝑑 (in feet) traveled by a projectile launched at an angle θ and with an initial speed 𝑣 (in feet per second) is given by 𝑑 =[v^2/32]sin2θ . Estimate the horizontal distance traveled by a football that is thrown at an angle of 20॰ with an initial speed of 20 feet per second.

• 108.2 ft

• 16.05 m

• 8.03 ft

• 120 ft

What is the reference angle of 225 degrees. Express your answer in degrees

• 60 degrees

• 30 degrees

• 135 degrees

• 45 degrees

Tags

CCSS.HSF.TF.B.7

What is the reference angle of 4pi/3. Express your answer in radians

• 5pi/3

• pi/3

• 2pi/4

• pi/6

Use your calculator to approximate the value of tan(280). Round to the nearest thousandths.

• 5.24

• -5.67

• 445.63

• 567.00

Tags

CCSS.HSF.TF.A.2

Use your calculator to approximate the value of sin(4pi/5)

• 1.2365

• 0.9587

• 0.2365

• 0.5878

Tags

CCSS.HSF.TF.A.4