SB Ch 4 answers.notebook
January 31, 2014
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SB Ch 4 answers.notebook
January 31, 2014
Section 4.1 Angles & Their Measures
DMS: Degrees-minutes-seconds is a way to measure angles
Each degree has 60 minutes and each minute has 60 seconds.
Example 1:
Convert 37.425 to DMS.
Convert 42 24'36'' to degrees.
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SB Ch 4 answers.notebook
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How many degrees is represented by 3π radians?
4
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Find the arc length of a circle given r = 6 and θ = π
π
4
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Sketch a diagram of a ship on the given course
150o 315o
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The captain of a ship follows a course of 50o for 5 miles and then changes to a 160o course for the next 10 miles. Draw a sketch of this trip.
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A and B are 300 nautical miles apart, how far is this in statute miles?
A and B are 300 statute miles apart, how far is this in nautical miles?
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p. 325
1 ­ 38 mod 4
40, 42, 43, 49, 50, 51
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3
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or √27
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Find all 6 trigonometric ratios for θ
13
5
θ
12
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50
θ
23
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Given sin θ = 2/3, find the other 5 trig ratios
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MEMORIZE!!!!!!!!!
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60
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From a point 340 feet away from the base of the Peachtree Plaza in Atlanta, the angle of elevation to the top of the building is 65O. Find the Height of the building.
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Homework: Page 335 #1-54 mod 4
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Angles greater than 360 or 2π
Find the following exact values using reference angles.
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WS with angles greater than 360 were given
maybe WS with solving was given as well?? after this section was
taught
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Reference Angles:
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Example 1: Find the following without a calculator:
sin 210
cos 135
tan 300
sin 360
tan 2π
3
cos 5π
4
sin 11π
6
tan 3π
2
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Page 347 # 25­42
finish 4.2 pg 335 #55, 56, 61 ,63
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Day 2: Exact Trig Values
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Example 2:
Example 3: Solve for all 0≤θ≤360 given sinθ = √ 3
2
**What would the answers be in radians?
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Day 2: Homework Page 347 #4-48 evens
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or f(x) = acos(bx + c) + d
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*
*
*
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Quick Review
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Evaluate without using a calculator
Cos (7π/3)
Cot (11π/6)
Sin (5π/2)
Csc (9π/4)
Tan (5π)
Sec (13π/4)
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Evaluate without using a calculator
Cos (7π/3)
Cot (11π/6)
Sin (5π/2)
Csc (9π/4)
Tan (5π)
Sec (13π/4)
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y = sin x
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y = cos x
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y = 2 sin x
y = sin (2x)
y = sin (x ­ π/4)
y = ­3 sin x
y = sin (x/2)
y = sin x + 2
y = 4 cos x
y = cos (3x)
y = cos (x + π/6) + 3
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Sketch a graph of y = 5 sin 2x
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Sketch a graph of y = 4 sin x/4
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Sketch a graph of y = ­2 sin (x ­ π/4) + 1
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Day 1:
Homework: Page 357 # 1-40 mod 3, 62-70 evens
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Warm Up
Sketch a graph of y = 5 sin 2x
Sketch a graph of y = 4 sin x/4
Sketch a graph of y = ­2 sin (x ­ π/4) + 1
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using rules for amplitude, period & frequency
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Write an equation to model this graph.
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Write two equations to model this graph.
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Write an equation to model this graph.
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Write two equations to model this graph.
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Write an equation to model this graph.
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Write two equations to model this graph.
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Day 2 Section 4.4 Story Problems
Page 355 in book
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Example: One particular July 4th in Galveston TX, high tide occurred
at 9:36 am. At that time, the water at the end of the 61st Street Pier
was 2.7 meters deep. Low tide occurred at 3:48 pm, at which time the
water was only 2.1 meters deep. Assume that the depth of the water is
a sinusoidal function of time with a period of half a lunar day (about 12
hrs 24 mins).
Create an equation to model this situation and answer the following:
a. At what time on the 4th of July did the first low tide occur?
b. What was the approximate depth of the water at 6:00 am and at
3:00 pm that day?
c. What was the first time on Jluy 4th when the water was 2.4
meters deep?
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A giant ferris wheel is 60 ft in diameter. The ferris wheel completes a revolution every 5 minutes. The closest the chair gets to the ground is 2 feet.
Write a function for the height a person is above ground t minutes after boarding.
How high above the ground is a person 13 minutes after boarding the ferris wheel?
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Homework: Page 358 # 73,79, 83-86
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Quick Review
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Remember: tanx = y
x
sine = y
cosine = x
Thus: tanx = sinx
cosx
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cotx = 1
tanx
cotangent = x
y
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Chart on pg 364
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Example: Describe y = -tan2x
Example: Describe the graph of y = 3cot(x/2) + 1
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Example: Find the value of x between π and 3π/2 that solves
secx = -2
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Homework: Page 365 # 13-20, 29-34
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Section 4.7 Inverse Trig Functions
Examples: Evaluate sin-1x without a calculator.
1
a. sin­1( )
2
3
­√
b. sin­1( )
2
π
d. sin­1( sin ( ))
9
1
c. cos­1( )
2
5π
e.sin­1( sin ( ))
6
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Example: Evaluate without a calculator.
a. cos (sin-1 (1/2))
b. arccos ( tan (π/4))
Example: Find the solution without a calculator.
a. tanx = -1
b. 2sinx = √2
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Homework: Page 385 #1-12, 23-32, 57-62
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Warm Up
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Example : A large, helium balloon is at the beginning of a parade
route awaiting the start of the parade. Two cables attached to
the underside of the balloon and make angles of 48 and 40
degrees with the ground and are in the same plane as a
perpendicular line from the penguin to the ground. If the cables
are attached to the ground 10 feet from each other, how high
above the ground is the balloon?
h
40
10
48
x
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Homework: Page 393 # 1,5,7,10,15,17,21,25,26,32-36,39-41,48
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