Trig in the Coordinate Plane
An angle theta is in quadrant 4.
Determine if sin and cos are positive or negative.
Cos is positive
Sin is negative
Jake is on a ferris wheel that has a radius of 30m. He starts in a cart at the far right of the wheel which is 40m off the ground.
What is the height of the lowest point on the ferris wheel?
10m
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. Find the height of the rider after 17 seconds. Round to the nearest hundreth.
h=28+22sin(9t)
37.99 meters
sin(theta)=5/13
in Quadrant 2.
Find
cos(theta)
cos(theta)=-12/13
Jake is on a ferris wheel that has a radius of 30m. He starts in a cart at the far right of the wheel which is 40m off the ground.
What is the height of the highest point on the ferris wheel?
70m
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. Find the radius and center height of the ferris wheel.
h=28+22sin(9t)
radius: 22m
center: 28m
sin(theta)=-sqrt(5)/sqrt(30)
in Quadrant 4.
Find
cos(theta)
cos(theta)=5/sqrt(30)
Jake is on a ferris wheel that has a radius of 30m. He starts in a cart at the far right of the wheel which is 40m off the ground.
From the starting point, the wheel rotates 50 degrees counterclockwise. Find Jake's new height.
62.98m
40+30sin(50)
The following equation models the height (in meters), h, of a rider on a ferris wheel after t seconds. How long does it take for the wheel to make one full rotation.
h=28+22sin(9t)
40 seconds
The terminal ray of an angle passes through the point
(-5, sqrt11)
Find
sin(theta) and cos(theta)
sin(theta)=sqrt(11)/6
cos(theta)=-5/6
Jake is on a ferris wheel that has a radius of 30m. He starts in a cart at the far right of the wheel which is 40m off the ground.
From the starting point, the wheel rotates 50 degrees counterclockwise. What other angle has the same height as the 50 degree angle?
130 degrees
(180 - 50)
Jake is on a ferris wheel that has a radius of 32m. He starts in a cart at the far right of the wheel which is 40m off the ground. It takes 90 seconds to complete one full rotation.
Write a function to model Jake's height after t seconds.
h(t)=32sin(4t)+40
The terminal ray of an angle passes through the point (-4, -3).
Find
sin(theta) and cos(theta)
sin(theta)=-3/5
cos(theta)=-4/5
Frankie is on a ferris wheel that has a radius of 40m. He starts in a cart at the far right of the wheel which is 45m off the ground. It takes 72 seconds to complete one full rotation.
Determine Frankie's height after 20 seconds. Round to the nearest hundreth.
84.39m