Standard # 1 TF1. Unit Circle
1) Convert
17𝜋
12
to degrees
2) Convert 1065° to radians
4) Find + / - co-terminal angle for # 1 above.
7𝜋
6
7) tan
=
5) sin(−
3) Find a reference angle for 600°
5𝜋
)
4
8𝜋
6) cos( 3 ) =
=
8) What quadrant is 𝜃 in if sin 𝜃 < 0 and cos 𝜃 > 0?
9) What quadrant is 𝜃 in if tan 𝜃 < 0 and sin 𝜃 > 0?
10) cos(−17𝜋) =
Standard # 2 IF7. Transformations of Graphs
1) 𝑓(𝑥) = 4𝑐𝑜𝑠(2𝑥) + 1
2) 𝑓(𝑥) =
3) 𝑓(𝑥) =
3
−2𝑠𝑖𝑛 (4 𝑥) − 3
𝜋
3𝑐𝑜𝑠 ( 2 𝑥) − 2.5
a) amplitude _______
b) period _______ c) frequency _______ d) midline ______
a) amplitude ________ b) period _______ c) frequency _______ d) midline _______
a) amplitude ________ b) period _______ c) frequency _______ d) midline _______
4) What is the period of the following function? __________
6) What is the amplitude of the following function? _________
8) What is the y intercept of the following function? ________
1
10) Graph the following function: 𝑓(𝑥) = 2𝑠𝑖𝑛 (2 𝑥) + 1
5) What is the midline of the function in # 4? _______
7) What is the frequency of the function in # 6? _______
9) What is the midline of the function in # 8? ________
Standard # 3 TF5. Graphing a Unit Circle
1) What is the equation that represents the following graph?
2) What is the equation that represents the following graph?
3) What is the equation that represents the following graph?
4) What is the equation that represents the following graph?
5) What is the equation that represents the following graph?
1
6) Graph the following: 𝑓(𝑥) = 2 𝑐𝑜𝑠(𝑥) + 1
1
𝜋
7) Graph the following: 𝑓(𝑥) = − 2 𝑐𝑜𝑠 ( 4 𝑥)
Standard # 3 TF5. Graphing a Unit Circle, continued
1
2
8) Graph the following: 𝑓(𝑥) = −3𝑐𝑜𝑠 ( 𝑥) − 4
9) When answering a Ferris wheel question, all graphs begin under/over the midline (circle one)
10) When answering a Ferris wheel question, all graphs are sine / cosine curves (circle one)
Standard # 4 BF4. Inverses of Functions
1) What inverse function is this?
2) What inverse function is this?
3) What inverse function is this?
4) Evaluate 𝑆𝑖𝑛−1 ( )
6) Evaluate 𝐶𝑜𝑠 −1 (−
√3
)
2
9) Solve: 2 sin 𝑥 + 1 = 0
12) 𝑠𝑖𝑛2 𝑥 − 3𝑠𝑖𝑛𝑥 = −2
1
2
7) Evaluate 𝑐𝑜𝑠 (𝑡𝑎𝑛−1
10) Solve: 3𝑡𝑎𝑛2 𝑥 − 1 = 0
√3
)
3
5) Evaluate 𝐴𝑟𝑐𝑡𝑎𝑛(−1)
1
8) Evaluate 𝑠𝑖𝑛 (𝑐𝑜𝑠 −1 (− 2))
11) Solve: 2𝑠𝑖𝑛𝑥𝑐𝑜𝑠𝑥 + 𝑐𝑜𝑠𝑥 = 0
Standard 5: SRT.9 Areas of Triangles
1) Find the area of triangle ABC when a = 8.4 cm, b = 3.7 cm and C = 44°
2) Find the area of triangle ABC when AB = 6.7 cm, AC = 9.3 cm and < BAC = 55°
3) A triangle of area 21.4 𝑐𝑚2 has two edges measuring 9.8 and 5.9 cm respectively. Find the angle between those two edges.
4) A triangle ABC has an area of 17.3 𝑐𝑚2 . AB = 6.3 cm and < BAC = 31.4° What is the length of the edge AC?
5) A new homeowner has a triangular – shaped back yard. Two of the three sides measure 53 ft. and 42 ft. and form an
included angle of 135°. To determine the amount of fertilizer and grass seed to be purchased, the owner has to know, or at
least approximate, the area of the yard. Find the area of the yard to the nearest square foot.
6) Find the area of the triangle drawn in the figure:
7) Find the area of the triangle drawn in the figure:
8) Find the area of triangle DEF if DE = 11 mi, EF = 6 mi, and FD = 9 mi.
9) Find the area of triangle QRP if QR = 11 m, QP = 10 m, and <RQP = 29°
10) Find the area of a triangular playground, to the nearest square meter, with sides of length, 10 m, 15 m, and 16 m.
Standard 6. SRT.10 Laws of Sines and Cosines
1) Two airplanes leave Berlin, one heading straight for London and the other straight for Paris. Use the Law of Cosines to
estimate the measure of the angle, 𝜃, they will form.
2) Find BC
3) Find JM
4) Find the measure of the smallest angle.
5) Find DE in triangle DEF if <D = 30°, <F = 64°, and DF = 17.
6) Find TA in triangle TAR if <R = 120°, AR = 18, and RT = 25.
7) Two lookout towers are 50 kilometers apart. The ranger in Tower L sees a fire at point C such that m<CLM = 40°. The ranger
in Tower M sees the same fire such that m<LMC = 65°. How far is the fire from Tower L? (Hint: draw a picture and label)
8) A baseball infield is determined by a square with sides 90 ft. long. In the diagram,
home plate is H and first base is F. Suppose the first baseman ran in a straight line
from F to catch a pop-up at B, 120 ft. from home plate. If the measure of <FHB is 10°
how far did the first baseman run?
9) Solve the following triangle ABC if <A = 31°, a = 22 and b = 9.
10) Solve the following triangle ABC if a = 6, <B = 14.3°, c = 25
Standard # 7. TF.9 Identities and use of Sum and Differences
1) Simplify cot 𝑥 sec 𝑥
2) Simplify
𝑐𝑠𝑐 2 𝑥− 𝑐𝑜𝑡 2 𝑥
𝑠𝑖𝑛2 𝑥
cot 𝑥
4) Simplify cos 𝑥(sec 𝑥 − cos 𝑥)
5) Simplify
7) Evaluate 𝑠𝑖𝑛(255°)
8) Evaluate 𝑐𝑜𝑠(630°)
tan 𝑥
3) Simplify 𝑠𝑖𝑛2 𝑥 ∙ 𝑐𝑜𝑡 𝑥 ∙ 𝑐𝑠𝑐 𝑥
6) Simplify
𝑡𝑎𝑛2 𝑥+1
1+ 𝑐𝑜𝑡 2 𝑥
9) Evaluate 𝑠𝑖𝑛(−150°)
7𝜋
10) Evaluate 𝑡𝑎𝑛 ( 12 )
Standard # 7. TF.9 Identities and use of Sum and Differences
1) Simplify cot 𝑥 sec 𝑥
2) Simplify
𝑐𝑠𝑐 2 𝑥− 𝑐𝑜𝑡 2 𝑥
𝑠𝑖𝑛2 𝑥
cot 𝑥
4) Simplify cos 𝑥(sec 𝑥 − cos 𝑥)
5) Simplify
7) Evaluate 𝑠𝑖𝑛(255°)
8) Evaluate 𝑐𝑜𝑠(630°)
7𝜋
10) Evaluate 𝑡𝑎𝑛 ( 12 )
tan 𝑥
3) Simplify 𝑠𝑖𝑛2 𝑥 ∙ 𝑐𝑜𝑡 𝑥 ∙ 𝑐𝑠𝑐 𝑥
6) Simplify
𝑡𝑎𝑛2 𝑥+1
1+ 𝑐𝑜𝑡 2 𝑥
9) Evaluate 𝑠𝑖𝑛(−150°)