Which Ratio?
Trig Values
Circles
Equations
Applications
100

Use it when you know the length of the hypotenuse and the adjacent leg.

What is Cosine?

100

The cosine of 0 degrees.

What is 1?

100

The area of a circle with radius 3.

What is 9pi?

100

The value of x on [0, 360) in degrees when 2sin(x) = -1 .

What are 210 and 330 degrees?

100

The maximum height that a 20 foot ladder can reach safely if we follow the suggestion that the ladder should not make an angle grater that 75 degrees with the ground.

What is 19.32 ft?

200

Use it when you know the hypotenuse and the opposite leg.

What is Sine?

200

The sine of 120 degrees.

What is sqrt(3)/2?

200

The circumference of a circle with diameter 10.

What is 10pi?

200

The value of on [0, 2pi] in radians when 4tanx - 11 = -7.

What is pi/4 and 5pi/4?

200

The distance above sea level after a plane ascends from 1 mile at a 3 degree angle for 60 ground miles.

What is 4.1 mi?

300

Use it when you know the two legs.

What is Tangent?

300

The cosine of 7pi/4 degrees.

What is sqrt(2)/2?

300

The area of a sector with radius 10 and central angle 90 degrees.

What is 25pi?

300

The value of x on [0, 360] in radians when 4secx + 12 = 20.

What is 60 and 300 degrees?

300

The angle of elevation of the sun when a 7.6 meter flagpole casts an 18.2 meter shadow, rounded to the nearest degree.

What is 22.7 m?

400

Use it when you know want to know the opposite leg and you know the measure of the angle and other leg.

What is Tangent?

400

The tangent of 5pi/4 degrees.

What is 1?

400

The arc length of a circle with radius 20 and central angle 3pi/4.

What is 15pi?

400

All values of x on [0, 2pi] in radians when 3cosx +1 = 10.  

What are no solutions?

400
The angle of depression of a sledding run 300 yards long with a vertical drop of 27.6 yards.
What is 5.3 degrees?
500

Use it when you want to know the opposite leg and you know the measure of the angle and hypotenuse.

What is Sine?

500

The cosecant of 270 degrees.

What is -1?

500

The area of a circle with radius pi.

What is pi3?

500

In degrees on [0, 360], this is when sinx = cosx.

What is 45 and 225 degrees?

500
The length of a ski run with a vertical drop of 1100 feet and angle of elevation of 24.4 degrees.
What is 2663 ft?