Unit 1A
Use a Trigonometric Identity to find cos(x) given that sin(x) = 3/5 where pi/2 < x < pi
Cos (x) = -4/5
Given that a Farris wheel has a function of g(x) = 45sin(15(x-pi)) + 50. Find the maximum and minimum.
max = 95 and min = 5
Find arcsin(-1/2). Only exact answers will be given credit. All others are wrong.
-pi/6
Use the Law of Sines and/or the Law of Cosines to find the missing side. Two sides and the included angle of a triangle measure 28 cm, 52°, and 40 cm. Round your answer to the nearest tenth. Then, explain the reason for your choice based on the given information.
a = 31.7
Which country produces the most coffee in the world?
Brazil
Determine if it is possible for a number x to satisfy the given conditions using a trigonometric identity.
sin(x) = 7/25 and cos(x) = 24/25
Yes
Name the phase shift and period of the following: y = -3cos(2x+pi/4) + 1
PS: -pi/8
Evaluate the arctan of (sqrt(3)/3). Only exact answers will be given credit.
-pi/6
Use the Law of Sines and/or the Law of Cosines to find all possible values for m < A. If necessary, round your answer(s) to the nearest whole degree. Then, explain the reason for your choice in terms of SSS, SAS, AAS, ASA, or SSA. In △ ABC, m < B = 32°, a = 8 in. and b = 6 in.
m < A = 45 and 135 degrees
About how many taste buds does the average human tongue have?
10,000
Find the exact value of sin for an angle in standard position where (5, 7) lies on its terminal side. Use mathematical language to explain how your calculations and representations support your thinking.
sin (x) = 7/root(74)
Write the equation of a tangent curve with a period of 3pi, a phase shift of 4pi, an amplitude of 6, and a vertical shift of 2.
y = 6 tan(1/3(x - 4pi)) + 2
Evaluate the sin(arccos(-24/25))
sin(x) = 7/25
A triangle has sides 9 cm, 11.4 cm, and 8.3 cm. What is the area of the triangle to the nearest square unit? Show the work that leads to your answer.
37 cm^2
Who discovered penicillin?
Fleming
State the angle measure in radians represented by 3.75 rotations counterclockwise. Leave your answer in terms of pi.
15pi/2
Write the equation of a sine curve with an amplitude of 7, period 6π, phase shift of -7.
f(x) = 7sin(1/3(x + 7))
Why can you not evaluate the sin(arcsin(8pi))?
Falls outside of the boundaries of inverse sine.
A triangle is given with two included sides measuring 26 and 28 cm, as well as an included angle of 123 degrees. What is the area of the triangle to the nearest square unit?
305 cm^2
Who starts first in chess? (What color?)
White
Determine two angles (one positive and one negative, in radian measure) coterminal to the angle: 7pi/4
-pi/4 , 15pi/4
How are the sine and cosine functions related. Give the smallest possible value of the transformation.
A PS of pi/2
Solve in Radians: -6 = 6cos(3x)
x = -pi/3
A bridge is to be built from the land to a point on an island. The only two places on the land to start the bridge are point X and point Y, 1200 m apart. Point X has better access to the lake but is farther from the island than point Y. From X you measure a 44 ̊angle from the land to the point on the island, and from point Y you measure a 60 ̊angle from the land to the same point on the island. To the nearest tenth of a meter, how much longer is the bridge if built from point X than if built from point Y?
211.9 m
Name the world’s biggest island
Greenland