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Right triangles
Radians
Word Problems
Waves
The Unit Circle
100
If the lengths of the sides of a right triangle are 3 inches, 4 inches, and 5 inches, this is sine of the smallest angle.
What is 3/5 ?
100
The method for converting degrees to radians.
What is multiply by pi/180 ?
100
Suppose a Ferris wheel has a diameter of 180 feet. The wheel rotates 20° each time a new passenger is picked up. How far would you travel when the wheel rotates 20°? Round your answer to the nearest tenth if necessary.
What is 31.4 feet?
100
The height of a wave from the midline to the top is called this.
What is amplitude?
100
The reference angle for 480 degrees
What is 60 degrees ?
200
If the lengths of the sides of a right triangle are 3 inches, 4 inches, and 5 inches, this is measure of the smallest angle (rounded to the nearset tenth of a degree)
What is 36.9 degrees
200
The measure of a right angle, in radians.
What is pi/2 ?
200
A water sprinkler sprays water on a lawn over a distance of 25 feet and rotates through an angle of 130 degrees. Find the area of the lawn watered by the sprinkler.
What is 709.04 square feet?
200
The period of the function f(x)= tan x
What is pi ? (or 180 degrees)
200
The reference angle for -500 degrees
What is 40 degrees ?
300
To the nearest tenth of a centimeter, the length of the hypotenuse when the leg opposite a 36-degree angle in a right triangle is 15 cm.
What is 25.5 cm ?
300
The measure of a 210-degree angle, in radians
What is 7pi/6 ?
300
A truck is moving at a rate of 105 kilometers per hour, and the diameter of its wheels is 1 meter. Find the angular speed of the wheels in radians per minute.
What is 3500 radians per minute?
300
Graph the function f(x) = -.5 * tan(2x) without using a calculator.
Period =pi/2; Asymptotes x = +/- pi/4; at x= +/- pi/8 f(x) = -/+ 1/2, f(0) = 0
300
The exact value of the sin of 135 degrees without using a calculator.
What is (square root of 2) / 2 ? ...... or 1 / (square root of 2)
400
A ladder leaning against a house forms a 65-degree angle with the flat ground. If the ladder is 20 feet long, this is how far the bottom of the ladder is from the house (to the nearest tenth of a foot).
What is 8.5 feet ?
400
The approximate number of degrees (rounded to one decomal place) equivalent to 1 radian
What is 57.3 degrees ?
400
A plane is 90 miles south and 110 east of London Heathrow Airport. What bearing should be taken to fly directly into the airport?
What is N 309.3 W?
400
The displacement from equilibrium of an oscillating weight suspended by a spring is given by y(t) = 1/4*cos(6t), where y is the displacement (in feet) and t is the time (in seconds). Find the absolute value of the difference in the displacements when t=0 and t=1/4.
What is .23 feet?
400
The exact value of cot(arcsin(3/8)) without the aid of a calculator.
What is (square root of 55) / 3 ?
500
From the top of a vertical cliff 50 m high, the angle of depression of a boat at sea is 12 degrees. To the nearest meter, how far is the boat from the base of the cliff?
What is 235 meters?
500
The high-dive champion executed 3.5 complete revolutions in his winning dive. This is the measure of his turn in radians.
What is 7*pi radians
500
A family drives down a straight stretch of highway for 12 miles. When they begin driving, a distant mountain can be seen 30° off to the right of the road. When they finish driving, the mountain now appears to be 60° to the right of the road. How far away is the mountain from them when they have finished driving?
What is 12 miles?
500
Write the equation for the simple harmonic motion of a ball on a spring that starts at its lowest point of 6 inches below equilibrium, bounces to mits maximum height of 6 inches above equilibrium, and returns to its lowest point in a total of 2 seconds.
d = -6 cos(pi*t)
500
The value of cot(x), given that sec(x)=-29/20 and sin(x)>0
What is -20/21?