Chapter four part A starts a very long journey into trigonometry. We will spend at least 14 weeks looking at trig functions and their applications but this first chapter examines the building blocks and definitions that we will use for the next three years. It is critical that you memorize these properties as soon as possible. As usual, please don’t put them in the short-term memory! Every day we will try and tie these concepts together and create a firm foundation for future studies. Please ask questions regularly in class or stop by to see me or go to the MathResourceCenter in room C117 for extra help.
1.4.1Radian and Degree Measures
p. 255-256#1-63 odd
2.p. 256-257#65-89 odd
3.p. 255Vocabulary Check: 1-10
p. 258#96-101
Angular and Linear Speed Worksheet
4.Unit Circle Activity
Memorize first Quadrant of the Unit Circle
5.4.2Trigonometric functions: the Unit Circle
p. 264#1-35 odd
6.4.2Trigonometric functions: the Unit Circle
p. 264-265#37-59 odd
4.3Right Triangle Trigonometry
p. 274# 3-15, multiples of 3
7.4.3Right Triangle Trigonometry
p. 274-275#17-51 odd
8.4.3p. 275-277#53-56 all, 57-65 odd
Review for Quiz Worksheet
9.Exact Values Worksheet
10.4.4Trigonometric Functions of Any Angle
p. 284-286#1, 5, 9, 13-16, 17, 21, 25, 27, 29-51 odd, 53, 55, 59, 61, 65, 69, 72, 81, 83, 93, 95
11.Chapter Review Sheet
p. 332Read through Chapter Summary for sections 4.1-4.4. What did you learn?
Nov 12-16 / #2 / #3 / #4UNIT CIRCLE / #5
4.1 Quiz
#9------ / #6
------>
Nov
19-23 / #7
------/ Exact Value Quiz
#8
------> / No School / No School / No School
Nov. 26-30 / #10 / 4.1-4.3 Quiz / Review
#11 / 4A Test
Honors Pre-CalculusName______
Chapter 4 Worksheet: Angular and Linear Speed
Directions for 1 and 2: Use the definition of radian to solve #1 and definition of linear speed to solve #2.
1.A highway curve, in the shape of an arc of a circle is .25 miles. The direction of the highway changes 45 degrees from one end of the curve to the other. Find the radius of the circle in feet that the curve follows.
2.The radius of the Earth is 4000 miles. What is the linear velocity of a point near the equator? (Hint, the earth revolves every 24 hours)
Directions for 3 -- 8: Use the use unit analysis to answer the following questions.
3.To the nearest revolution, how many times will a bicycle wheel measuring 26 inches in diameter turn if it is ridden for one mile?
4.If the wheel of the bicycle in the previous problem turns at a constant rate of 2.5 rev/sec, what is its linear speed in ft/s? How about in mph?
5.If a wheel with a 16 inch diameter is turning at 12 rev/sec, what is the linear speed of a point on its rim in ft/min?
6.The crankshaft pulley of a car has a radius of 10.5 cm and turns at rad/sec. What is the linear speed of the pulley?
7.Find to the nearest cm/sec the linear speed of a point on the rim of a wheel of radius 24 cm turning at an angular speed of rad/sec.
8.The linear speed of a point 15.3 cm from the center of a phonograph record is cm/sec. What is the angular speed of the record in rad/sec?
Bonus: Find the coordinates of the final position of a point P moving counterclockwise in uniform circular motion at rad/sec if P starts at the point ( 5 , 0 ) and moves for 14 seconds.
H-Pre-Calculus
Chapter 4A
Targets
Section 4.1
1. I can sketch a positive or negative rotation and find co-terminal angles.
Determine the quadrant that each angle lies and find a positive and a negative coterminal angle.
a.b.c.
d.e.f.
Determine the quadrant that each angle lies and find it’s supplement and complement (if possible).
g.h.i.
2.I can convert between degrees/radians and between D°M’S’’/decimal degree.
Convert the following angle measuresfrom degrees to radians.
a.153ob.521.5oc.-71o
Convert the following angle measuresfrom radians to degrees.
d.e.f.
Convert the following angle measures to D°M’S’’
g.153.658oh.521.5oi.-71.123o
3.I can define radians in terms of arc length and radius and solve for unknowns.
Find the length of the arc intercepted by a central angle with the given radius.
a.b.
4. I can convert between angular and linear speed using unit analysis.
a.The cylindrical roller on highway roller has a 48 inch diameter and makes .7 revolutions per
second. Find the angular speed of the roller in radians per second and find the linear speed of the roller.
b.The tire on a car has a radius of 16 inches and is spinning at a rate of 4 revolutions per second.
Find the angular speed of the roller in radians per second and find the linear speed in mph.
Section 4.2
5.I can define and evaluate the six trig functions in terms of x and y on the unit circle.
Evaluate the six trigonometric functions of the real number.
a.b.c.
6. I can identify which trig functions are odd and which are even and, given a trig value at some angle “t,” I can evaluate related trig functions at “-t.”
a.Identify the trig functions are odd and which are even. Use a specific example of each function to verify your identification.
b. If, then = ?
c. If, then = ?
7.I can identify the “important” angles (degree and radian) and the (x, y) coordinate on the unit circle.
a.Draw a unit circle and complete the important points – degree, radian, and (x, y) points.
b. Evaluate exactly .
Section 4.3
8. I can use a triangle and 2 given sides to evaluate the six trig functions.
Find the exact values of the six trigonometric functions of the angle θ.
a.b.
9. I can simplify and evaluate trig expressions using the fundamental trigonometric identities (6 complementary, 6 reciprocal, 2 quotient identities and 3 Pythagorean identities).
a.Given in a right triangle, determine the other five trig functions.
b.Given in a right triangle, determine the other five trig functions.
c.Given in a right triangle, find , an
10. I can use inverse trig functions to find Ө in both radians and degrees by memory or with a calculator.
Evaluate exact values for θ when possible, otherwise use a calculator. Give both the degree & radian measure. Assume θ is in the first quadrant.
a.b.c.
d.e.f.
11. I can evaluate trig functions at a given angle by memory or with a calculator.
Find exact values for θ when possible, otherwise use a calculator. Assume θ is in the first quadrant.
a.b.c.
d.e.f.
12. I can solve real world trig problems with sine, cosine and tangent
a.A person standing 100 meters from the base of a vertical tower places a transit on the ground and determines the angle of elevation to the top of the tower is 4.749o. Determine the height of the tower.
b.A building has a row of lights around the sides of the building 30 feet below the top of the building. A marker on the street that approaches the building notes that the angle of elevation to the top of the building is 10o and the angle of elevation to the row of lights is 6o. How far from the building is the marker on the street and how tall is the building?
c.The sonar of a navy cruiser detects a submarine that is 7000 feet from the cruiser. The angle between the water level and the submarine is 25o. How deep is the submarine?
Section 4.4:
13. I can determine the six trig functions exact value given a point on the terminal side of an angle in standard position.
a.Given the point ( 5, -7 ) on the terminal side of an angle, determine the six trig functions.
b.Given the point ( -6, -4 ) on the terminal side of an angle, determine the six trig functions.
c.Given the point ( -3, 8 ) on the terminal side of an angle, determine the six trig functions.
14. I can evaluate trig values given one value and other information.
a.Given and , evaluate and .
b.Given and , evaluate and .
c.Given and θ is in Quadrant II, evaluateand .
d.Given and θ is in Quadrant IV, evaluateand .
e.Find Ө if and (remember, there should be two answers!)
15. I can find and sketch the reference angle of a rotation.
Find the reference angle of each of the following.
a.θ = 315ob.θ = 16.7c.θ = -30.2d.
16. I can use trig identities to find other trig values given information about one trig value.
Use the Pythagorean identities to evaluate each of the following.
a.Given and , evaluate and .
b.Given and , evaluate and .
c.Given and θ is in Quadrant II, evaluateand .
d.Given and θ is in Quadrant IV, evaluateand .
H-Pre-Calculus
Chapter 4A Target Answers
1a.
1b.
1c.
1d.
1e.
1f.
1g.
1h.
1i.
2a.2.670
2b.9.102
2c.-1.239
2d.128.5710
2e.4320
2f.-315.1270
2g.153039’28.8”
2h.521030’0”
2j.-71o7’22.8”
3a.s = 7.854 in
3b.s = 36.233 ft.
4a.
4b.
5a. / 5b. / 5c.sin(t) / / /
cos(t) / / /
tan(t) / / /
cot(t) / / /
sec(t) / / /
csc(t) / / /
6a.even: cosine, secant
Odd: sine, tangent,
cotangent, cosecant
6b.-3
6c.
7a.See your unit circle
7b.
8a. / 8b.sin(θ) / /
cos(θ) / /
tan(θ) / /
cot(θ) / /
sec(θ) / /
csc(θ) / /
9. / a / b.
sin(θ) / /
cos(θ) / /
tan(θ) / /
cot(θ) / /
sec(θ) / /
csc(θ) / /
9c.
10a.
10b.
10c.
10d.
10e.
10f.
11a.
11b.
11c.
11d.
11e.
11f.
12a.8.308 meters
12b. 421.214 feet, 4.271 feet
12c.2958.328 feet
13. / a. / b. / c.sin(θ) / / /
cos(θ) / / /
tan(θ) / / /
cot(θ) / / /
sec(θ) / / /
csc(θ) / / /
14a.,
14b.,
14c.
14d.
14e.105o or 285o
15a.45o
15b.0.992 radians
15c.1.216 radians
15d.
16a.see 14a
16b.see 14b
16c.see 14c
16d.see 14d