| 3a, 3b, and 3c | 3c (cont.) & 3d | 3d (cont.) & 3e | 3f | 3g |
|---|---|---|---|---|
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-11π/6
Find an angle in the interval [0, 2π] that is coterminal to the angle -π/6. Your answer does not need to be simplified.
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cosθ = 1/20
cos(-θ) = 1/20 sinθ = -sqrt(1-(1/20)^2) cotθ = -(1/20)/(sqrt(1-(1/20)^))
Let sec(θ) = 20 and let θ be in Quadrant IV. Find the following, in any order: sin(θ), cos(θ), cot(θ), and cos(−θ)
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θ = 2π - 0.8
θ = -0.8 θ = -2π+0.8
Given that sin(0.8)=0.7 (approximately), find all three other angles θ in the interval [−2π,2π]
such that sin(????)=0.7. Show all your work. |
A function that repeats a pattern over and over.
examples: daily temperature, DNA, breathing, sound, etc.
What is a periodic function? Give some real life examples.
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arcsin D: [-1,1], R: [-pi/2, pi/2]
arccos D: [-1,1], R: [0,pi]
What is the domain and range of arcsin and arccos
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(24*180)/π
Suppose that on a circle of radius 10, the angle θ intercepts an arc of length 240. What is the measure of the angle, in degrees? Your answer does not need to be simplified.
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30-60-90
45-45-90 Bonus: find sin(60) and sin(45)
Using a drawing define both special right triangles.
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tan(22) = h/(70+x)
tan(35) = h/x
At point A you measure the angle of elevation to a mountain and find that it is 22°. Then you walk 70 meters toward the mountain and measure the angle of elevation from point B and find it is 35°.
Set up, but do not solve, a system of two equations that can be used to find the height of the mountain |
See board for answer
Draw out the sinx, cosx, -sinx, -cosx
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arcsin: [-pi/2, pi/2]
arccos:[0,pi] arctan: (-pi/2, pi/2)
What are the restricted domains of arcsin, arccos, and arctan?
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cosθ = 2/3
sinθ = -(sqrt5)/3 or sqrt(1- (2/3)^2) tanθ = -((sqrt5)/3)/(2/3) secθ = 1/(2/3) cscθ = -1/((sqrt5)/3) cotθ = -(2/3)/((sqrt5)/3)
Suppose that we are told that θ is an angle in Quadrant IV and cos(θ) = 2/3
Find all six trig functions. You may leave your answer unsimplified, in calculator-ready form. You may not use a calculator or anything we have not yet learned. |
Complementary angles have a sum of 90* or pi/2
Define complementary angles
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40tan76
You're standing 40m from Herty Hall and find that the angle of elevation to the top of Herty Hall is 76*. What is the height of Herty Hall.
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See board for answer
Draw a graph of y=cos(x+pi)
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arcsin(-1) = -pi/2
arcsin(-sqrt3/2) = 5pi/3
What is the value of arcsin(-1)? What is the value of arcsin(-sqrt3/2)?
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0, pi, 2pi (there are infinitely many answers)
Bonus: How does this relate to the sine function as a wave?
Find three angles in radians with a sine value of 0.
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sin(a) = cos(90 - a)
cos(a) = sin(90 - a) tan(a) = cot(90-a) cot(a) = tan(90-a) sec(a) = csc(90-a) csc(a) = sec(90-a)
Define and list the cofunction identities.
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cos(60) = 1/2
Using a special right triangle find cos(60)
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See board for answer
Graph 2sin(4(x-pi)
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x = -1/4
Solve for x:
arcsin(2????)=(−????/6) |
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cos(t) = sqrt(1-(1/5)^2)
sin(t) = 1/5
Use the Pythagorean identities to find sin(t) and cos(t) given that csc(t) = 5 and t is in quadrant II.
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sin(15*)
Using a cofunction identity cos(75*) = ________
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Sine is opposite over hypotenuse or y/r so the corresponding lengths of the triangle should measure 3 and 4 units to find sin(t).
Draw a triangle with angle t satisfying sin(t)=3/4. Explain how you know sin(t)=3/4.
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-2cos(x+(pi/2))
2sinx -2sin(x+pi) 2cos(x-(pi/2))
Find all four equations that fit the graph with points
(0,0) (pi/2,2) (pi,0) (-3pi/2, -2) (2pi,0) |
θ=arctan(200/400)
Suppose from the top of the SkyView Ferris Wheel, 200 feet high, you see your friend on the ground. Your friend texts you to say that she is exactly 40 feet from the base of the Ferris Wheel. What is the angle of elevation θ from your friend to you? Leave your answer in calculator-ready form, but it must be of the form θ=
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