Radian Measure
How many radians are in a full circle?
2π
How long is the diameter of the unit circle?
2 units long
Which characteristic of the sine and cosine graph shows how many complete cycles are contained in an interval of length 2π?
Frequency
What is the altitude of an equilateral triangle with a side length of 4?
2√3
Which trigonometric function is positive for angles in Quadrant IV?
Cosine
What is the approximate measure in degrees of an angle of 1 radian?
Approximately 57°.
The point where the terminal side of angle A, which is in standard position, crosses the unit circle has coordinates (0.87,-0.48). What is the Quadrant of angle A?
Quadrant IV.
What is the amplitude of the function y=-4cos(2x-5)+3?
4
Two sides of a right triangle are 4 and 8. What is the longest possible third side of the right triangle?
4√5?
In a right triangle, the two acute angles are \alpha = 2x + 1 and \beta = 3x - 6 . What is the value of x?
x = 19
What is the measure in radians of an angle of 120°?
(2π)/3
The point where the terminal side of angle B, which is in standard position, crosses the unit circle has a coordinates (sqrt3/2,a). If angle B is a Quadrant I angle, what is the value of a?
1/2
What is the period of the function y=3cos(4pix-6)-7?
1/2
If tan(x) = ⅔ what is cos(x)?
cos(x) = 3/√13
The terminal side of angle M crosses the unit circle at a point with coordinates (0.8,-0.6). What is the tangent of angle M? Round to the nearest hundredth.
-0.75
A central angle in a circle subtends an arc of 10 units. What is the measure of the central angle in radians if the radius of the circle is 18 units long?
5/9
Angle C is a Quadrant III angle and the point where its terminal side crosses the unit circle has coordinates (b,b). What is the measure, in degrees, of angle C?
225°
What is the maximum value of the function y=4sin(2x+3)+5?
9
A 10-foot ladder leaning on a wall reaches a height of 9 feet above the ground. What is the angle the ladder makes with the ground? Round to the nearest whole angle.
64°
A cosine function has a period of 4. How many complete cycles of this function occur on an interval of length 2π?
π/2
A central angle in a circle is 80°. What is the length of the subtended arc if the radius of the circle is 6 units?
(8π)/3
Angle D is a Quadrant I angle and tan(D)=1. What are the coordinates of the point where the terminal side of the angle crosses the unit circle?
(sqrt2/2,sqrt2/2)
What is the equation of a sine function with an amplitude of 1/2, a period of 6, and a midline of y=-4, assuming there is no phase shift.
There are two possibilities,
y=1/2sin(pi/3x)-4
or
y=-1/2sin(pi/3x)-4
Standing on the roof of her building, Kara can see the top of the building across the street looking up at an angle of 30˚. She knows the build is 150 ft away from where she's standing and her own building is 100 ft tall. How tall is the the building across the street?
150*TAN(30˚) + 100 = 186 ft
Angle A is a Quadrant I angle. If it is true that sinA<cosA, what is one possible measure of angle A?
any angle between 0° and 45°