100% Unit Test Review: Trigonometry
What is the exact value of tan(19pi/12)?
-2 - sqrt 3
Based on the sketch below, how far is Joey's house from the park?
0.86 mi.
From where Kiana is standing, she must look up at a 50° angle to see the top of a building. If she backs up 50 feet, she will need to look up at a 40° angle to see the top of the same building. Approximately how tall is the building?
141.8 ft.
Review the proof of cos(A - B) = cosAcosB + sinAsinB. Which of the following complete step 4 of the proof?
2 and 1
Let sin(2x) = cos(x), where 0° ≤ x < 180°. What are the possible values for x?
30°, 90°, or 150°
What is the area of triangle ABC? Round to the nearest square unit. Heron's formula: Area = sqrt s (s-a)(s-b)(s-c)
33 square units
The bottom of a 12-foot ladder is placed on the ground 7 feet from the base of a pipe sticking out of the ground. The top of the ladder is placed an unknown distance off the ground, leaning on the pipe. The ladder and the ground meet at a 56.4° angle. At what angle does the pipe meet the ground?
87.9°
Triangle RST has sides measuring 22 inches and 13 inches and a perimeter of 50 inches. What is the area of triangle RST? Round to the nearest square inch. Heron's formula: Area = sqrt s (s-a)(s-b)(s-c)
95 square inches
Which expression is equivalent to cos(pi/12)cos(5pi/12) + sin(pi/12)sin(5pi/12)?
cos(-pi/3)
What are the solutions to the equation sin(x+7pi/2) = -sqrt3/2 over the interval [0, 2pi]?
pi/6 and 11pi/6 only
Which equation could be used to solve for the measure of side q in triangle QRS below, given s = 15, S = 45°, and Q = 105°?
q/sin105° = 15/sin45°
Which shows a correct simplification of sin(x + pi)?
sin(x + pi) = sin(x)cos(pi) + cos(x)sin(pi) = sin(x) · -1 + cos(x) · 0 = -sin(x)
Which pair of equations below is a result of constructing the altitude, h, in triangle ABC?
sinA = h/c sinC = h/a
Review the diagram of the unit circle. Based on the diagram, which equation can be simplified to derive the cosine sum identity?
sqrt(cos(u+v)-1)^2+(sin(u+v)-0)^2=sqrt(cos(u)-cos(-v))^2+(sin(u)-sin(-v))^2
What is the exact value of sin(105°)?
sqrt2 + sqrt3/2
