Right Triangles
Trigonometric Functions/Identities
The Unit Circle
Drawing Angles
Angle Measures
100
What names do we label the three sides of a right triangle when there is a specific angle theta?
Opposite, Adjacent, and Hypotenuse
100
What are the names of the six trigonometric functions?
Sine
Cosine
Tangent
Cosecant
Secant
Cotangent
100
What is the center and radius of the unit circle?
radius=1
Center = (0,0)
100
What side of an angle drawn in standard position determines the direction it points?
The terminal side
100
How many degrees and how many radians are in one revolution of a circle?
360 degrees
2 pi radians
200
What are the names of the three angles in the triangle shown?
200
Which trig function is a reciprocal to the sine?
Which trig functions is a reciprocal to the cosine?
sine's reciprocal is the cosecant
cosine's reciprocal is the secant
200
What are the four quadrantal angles?
0, pi/2, pi, 3pi/2, 2p1
200
Angle 127 degrees points to which quadrant?
Quadrant 2
200
Find one positive and one negative angle that are coterminal to the following:
alpha=90^@
infinitely many answers!
... -1350, -990, -630, -270, 450, 810, 1170, 1530, ...
300
If one short leg of a right triangle is measures to 1.2 inches and the hypotenuse is 1.3 inches find the length of the other leg.
.5 inches
300
if
sin(theta)=2/7
then what is
cos(90^@-theta)
cos(90^@-theta) = 2/7
300
What are the important reference angles for anything found in the unit circle?
pi/6, pi/4, and pi/3
300
Determine which (if any) of the pairs of angles are coterminal or not.
i.) -400 degrees and 320 degrees
ii.) -40 degrees and -320 degrees
iii.) 400 degrees and -1040 degrees
i and iii are coterminal angles
300
Find one positive and one negative angle that are coterminal to the following:
alpha=(28pi)/9
infinitely many answers!
... (-44pi)/9, (-44pi)/9, (-26pi)/9, (-8pi)/9, (10pi)/9, (46pi)/9, (64pi)/9, (82pi)/9, ...
400
12.1208 feet
400
if
sin(theta)=7/25
find
cot(theta)
cot(theta)=24/7
400
convert
(3pi)/4
into degrees
135^@
400
What is the reference angle for
theta=(5pi)/7
theta'=(2pi)/7
400
What is the reference angle for
theta=(2pi)/7
theta'=(2pi)/7
500
A 15 foot ladder is leaning against the side of a house at a 65 degree angle. What is the distance from the house to the base of the ladder? (4 decimals)
6.3393 feet
500
if
sin(theta)=3/5
find the other five trig functions for
theta
cos(theta)=4/5
csc(theta)=5/3
cot(theta)=4/3
tan(theta)=3/4
sec(theta)=5/4
500
What quadrant does the following angle point?
theta=(-31pi)/11
Quadrant 3
500
Convert 285 degrees into radians
(19pi)/12