Standard Angles/Coordinates
Exact Values
Arc Length/Reference Angles
Converting Angles/Coterminal Angles
Sinusoidal Graphs
100
Find the angle (in degrees) that gives this coordinate point.
135°
100
What is cos(540°) ?
-1
100
What is a reference angle?
The angle between the terminal ray and the x-axis that is positive and acute (less than 90° or less than
pi/2 radians
100
What is a coterminal angle?
An angle that shares the same terminal ray, that you add or subtract a circles angle to find.
100
What is the amplitude, midline, and period of a periodic function.
Amplitude: |A| or the distance between the max and midline or midline and minimum.
Midline: k or (maximum + minimum) divided by 2
Period:
(2pi)/abs(B)
The distance it takes for a full cycle of a periodic function to complete.
200
Draw the angle 285° on a unit circle.
200
What is sin((7pi)/6) ?
-1/2
200
What is the arc length of a circle that has a radius of 3 inches and that has an angle of pi/6 radians?
pi/2
inches or 1.571 inches
200
Convert this angle into degrees. (5pi)/8
112.5°
200
Draw the 3 basic trig functions (sine, cosine, and tangent) and label some key points on the graph.
300
What is the angle (in radians) on the circle with the coordinate of (1/2,-sqrt3/2)
(5pi)/3
300
What is tan((3pi)/2) ?
Undefined
300
What is the reference angle for (5pi)/4 ?
pi/4
300
Find a coterminal angle for (5pi)/6 that is in between -2pi and -4pi.
-17pi/6
300
What is the amplitude, midline, period, and range of this periodic function?
Amplitude: 3
Midline: y=4
Period: pi
Range: [1,7]
400
What angle between -180° and -360° that shares the same sine value for 80° ?
-280°
400
What is the exact value of cos((-23pi)/6) ?
sqrt3/2
400
What is the arc length of a circle with a radius of 12 feet and an angle of 280°?
(56pi)/3 feet or 58.643 feet
400
Convert this angle from degrees to radians. Use a exact, simplified answer.
630°
(7pi)/2
400
What is the amplitude, midline, period, horizontal shift, and range of this periodic function?
y=-4cos(3(x+pi/4))-2
Amplitude: 4
Midline:y=-2
Period: (2pi)/3
"Horizontal Shift": -pi/4 " or left " pi/4
Range: [-6,2]
500
What is the coordinate for this angle on the circle?
(28pi)/3
(-1/2,-sqrt3/2)
500
Given the cos(theta)=4/5 and the angle theta is in Quadrant IV. What is sin(theta) and tan(theta) of the angle theta
sin(theta) = -3/5
tan(theta) = -3/4
500
What is the reference angle for (-4pi)/3 ?
pi/3
500
Which of these angles are coterminal?
(5pi)/4, -(5pi)/4,(13pi)/4, and -(3pi)/4
(5pi)/4,(13pi)/4, and -(3pi)/4
500
Given the following information about this trig function and write the equation.
"Sine Function, Amplitude: 6, Period of": pi/4,
"Horizontal Shift right" pi/6, "and Midline" : -3
y=6sin(8(x-pi/6))-3