Degrees, Radians and DMS
Trig Functions of Acute Angles
Periodic Functions
Graphs of Sine and Cosine
Problem Solving
100
Convert 3pi/7 to degrees. Round to the nearest hundredth of a degree.
77.1 degrees.
100
For an acute angle, A, in a right triangle, the ratio of the length of the opposite leg to the length of the hypotenuse.
sinA
100
Two angles are ___________ if they have the same initial side and terminal side, but have different measures.
Coterminal
100
A function that can be written in the form: f(x) = a sin(bx + c) + d
A sinusoid
100
To the nearest inch, find the perimeter of a 10-degree sector cut from a circular disc of radius 11 inches.
24 inches.
200
Convert 24 degrees into radians. Reduce your answer to the simplest fraction.
2pi/15
200
Find cosA and tanA if sinA = 5/13.
cosA = 12/13; tanA = 5/12.
200
Find one positive and one negative angle that are coterminal with -142 degrees.
+218 degrees; -502 degrees (other coterminal angles acceptable, also)
200

A sinusoidal function f(x) = a sin (bx) + c has a period of pi. What does this represent on the graph?

It represents that the function completes one full cycle within pi.

200
It takes ten identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track? Hint: Pick arc lengths.
approximately 5.4 inches
300
Use the appropriate arc length formula to find the arc length if the radius is 5ft and the central angle measures 18 degrees.
pi/2 ft
300
WITHOUT using a calculator, evaluate sec(pi/3).
2
300
Find the six trig functions of angle A, whose terminal side contains the point (-8,15).
sinA = 15/17; cosA = -8/17; tanA = -15/8 cscA = 17/15; secA = -17/8; cotA = -8/15
300
The amplitude of the function f(x) = 1/2 cos X is 1/2. How does that affect the graph?
It vertically shrinks the curves by a factor of 1/2.
300
The concentric circles on an archery target are 5 inches apart. The inner circle (red) has a perimeter of 41.416 inches. What is the perimeter of the next-largest (yellow) circle?
approximately 72.83 inches.
400
Convert 118.32 from decimal form to DMS.
118 degrees, 19 mins, 12 sec
400

Find acute angle A in degrees AND radians, such that cotA = 1.

45 degrees; pi/4 radians

400

WITHOUT a CALCULATOR or REFERENCE, find the 6 trig functions of 2pi/3.

sin(2pi/3) = sqrt3/2; cos(2pi/3) = -1/2; tan(2pi/3) = -sqrt3 csc(2pi/3) = 2sqrt3/3; sec(2pi/3) = -2; cot(2pi/3) = -sqrt3/3

400
The frequency of the function f(x) = 4 sin(2x/3) is 1/(3pi). How many cycles are completed in 2pi units?
2/3; frequency is (2/3)/2pi = 1/(3pi)
400
Kirsten places her surveyor's telescope on the top of a tripod of 6 feet above the ground. She measures a 9 degree elevation above the horizontal to the top of a tree that is 125 feet away. How tall is the tree?
approximately 25.8 feet.
500
Convert 48 degrees, 30 mins, 36 sec from DMS to degrees.
48.51 degrees
500
A guy wire from the top of a transmission tower forms a 75 degree angle with the ground at a 55 ft distance from the base of the tower. How tall is the tower?
205.26 ft.
500
Find secA and cscA if cotA = -4/3 and cosA < 0
secA = -5/4; cscA = 5/3
500
List how f(X) = -2 sin(4X) + 1 transforms the graph of f(X) = sinX
a = -2, so the amplitude shifts from 1 to 2, stretching it vertically by a factor of 2, as well as reflecting across the x-axis. b = 4, so the period changes from 2pi to pi/2, shrinking it horizontally by a factor of 1/4. d = 1, so it shifts the entire graph vertically up 1 unit.
500
What would be a function to represent a Ferris wheel whose center is 45 feet off the ground and takes 40 seconds to make one full rotation?
f(x) = sin (Xpi/20) + 45
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