Chapter 5
Let θ be an acute angle in a right triangle. If the hypotenuse is 13 units in length and the opposite side is 5 units in length, find the value of sinθ.
What is sinθ = 5/13?
State the double angle identity for the sine function.
What is sin(2x) = 2sinxcosx?
Use trigonometric form to find the cube roots of i.
What are -i, -√(3)/2 + i/2, and √(2)/2 + i/2?
Given the equation of a conic section, determine what type it is without completing the square. y = 4x^2 + 2x - 3y^2 - 14 = 0
What is a hyperbola?
Convert 7π/4 radians to degrees.
What is 315 degrees?
Find the exact value of cos(5π/4).
What is -√(2)/2?
State the fundamental identity.
What is (sinx)^2 + (cosx)^2 = 1?
Simplify the expression by using trigonometric form and DeMoivre's Theorem. Express your answer in the form a + bi. (-2+2i√(3))^4
What is -128 + 128i√(3)?
Given the equation of a conic section, determine what type it is without completing the square. 4x^2 - 2xy -x + y = 0
What is a hyperbola?
Find the quadrant containing x if x is in standard position. sinx >0 and tanx <0
What is Quadrant II?
Given cosx = 3/5 and x is in QIV, find the value of cotx.
What is cotx = -3/4?
Use an identity to find the exact value of cos(π/12).
What is √(2+√(3))/2?
Find the dot product of the vectors <4, -2> and <3, 7>.
What is -2?
Given the circle (x - 2)^2 + (y + 4)^2 = 64, find the center and the radius.
What is Center (2, -4) and radius 8?
Find the length of an arc that subtends an angle of 135 degrees on a circle of diameter 10 centimeters. Your answer must be exact.
What is 15π/4 cm?
Find the amplitude, range, domain, period, and phase shift of the given function. y = 4sin(3x-6π)-5
What is amplitude = 4, range [-9, -1], domain (-∞,∞), period = 2π/3, and phase shift = 2π?
Given two acute angles, A and B, and sinA = 3/8 and secB = 12/5 , find the exact value of sin(A - B).
What is sin(A - B) = (15 - √(6545))/96?
Are the vectors <2, 4> and <-2, 1> orthogonal to each other?
What is yes?
Given the conic section (x^2)/4 - (y-2)^2/16 = 1, find the coordinates of the foci.
What are (2√(5), 2) and (-2√(5), 2)?
Find all solutions to the equation 1/2(sinx)^2 = 1/4. Express your answers in radians.
What is (2k+1)π/4, where k is any integer?
OR
What is π/4 + (π/2)k, where k is any integer?
Different types of granular substances naturally settle at different angles when stored in cone-shaped piles. This angle is called the angle of repose. When rock salt is stored in a cone-shaped pile 11 feet high, the diameter of the pile’s base is 34 feet. Find the angle of repose for rock salt to the nearest tenth of a degree. How tall is a pile of rock salt that has a base diameter of 40 feet? Round to the nearest tenth of a foot.
What is the angle of repose is 32.9 degrees; and what is the pile is 12.9 feet tall?
Given two acute angles, A and B, and cosA = 3/4 and cscB = 8/3, find the exact value of cos(A + B).
What is cos(A + B) = (3√(55) - 3√(7))/32?
Two ships leave from the same port at the same time. The angle between their paths is 60 degrees. If the first ship travels at 30 mph and the second ship travels at 20 mph, what is the distance between the ships after 2 hours?
What is 20√(7) miles?
Given the conic section r = 1/(3 - 6cosθ), find the eccentricity and the equation of the directrix.
What is an eccentricity of 2 and a directrix of x = -1/6?
The leaning tower of Pisa was originally perpendicular to the ground and 179 feet tall. Because of sinking into the earth, it now leans at a certain angle x from the perpendicular. When the top of the tower is viewed from a point 150 feet from the center of its base, the angle of elevation is 53.3 degrees. Approximate the angle x to the nearest tenth of a degree.
What is x = 5.5 degrees?