MATH 165 – Chapter 6 - TOPICS and practice – Use a basic calculator unless indicated otherwise
Section 6.1
1) Vocabulary
• Angle:
o Initial Side
o Terminal Side
o Vertex
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•
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Positive angle (counterclockwise rotation)
Negative angle (clockwise rotation)
Standard position of an angle
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Angle that lies in a quadrant
Quadrantal angle
Central Angle
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Units of measurement of angles:
o Degrees
o Radians
2) Relationships between degrees, minutes and seconds
a) Convert an angle from degrees to degrees, minutes and seconds
i) 35.76 degrees to DMS -
b) Convert an angle from degrees, minutes and seconds to degrees
i) 56 º 35’ 40” to Degrees -
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3) Relationships between degrees and radians
a) Convert from degrees to radian – write (1) exact answer in terms of pi; (2) decimal approximation to
nearest hundredth
i)
125 º
ii) 456.2 º
b) Convert from radians to degrees – round the answer to the nearest hundredth.
i) 3pi/8
ii) 4
iii) -4pi/9
iv) 7
c) How many degrees are there in 1 radian?
Section 6.2
4) The six trigonometric functions: triangle approach
5) The six trigonometric functions: unit circle approach
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6) Trigonometric functions of quadrantal angles – use the unit circle approach (#21-30, 6.2)
7) Find the exact value of the trigonometric functions of special angles (#47-64, 6.2)
8) Given a point in the unit circle, find the exact values of the six trigonometric functions of the
corresponding central angle (#13-20, 6.2)
a) P(-1/5, 2sqrt(6)/5)
b) P(-sqrt(5)/3, -2/3)
9) Given a point on the terminal side of an angle, find the exact value of the six trigonometric functions
(#277-84, 6.2)
a) P(-2, 3)
b) (4, -5)
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10) Find the exact value of trigonometric expressions (#31-46, 6.2)
a) Csc(pi/2) + cot(3pi/2)
b) 2sin(pi/4) + 3 tan (5pi/3)
11) Find the approximate value of trigonometric expressions using the calculator (#65-76, 6.2)
a) Csc(32°)
b) cot(2)
c) sec(322°)
12) Trigonometric functions: FUNCTION NOTATION:
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13) Trigonometric functions: FUNCTION NOTATION:
14) Trig – function notation - operations
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15) Word problems: evaluation type
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Section 6.3 – Properties of Trigonometric Functions
16) Domain, range and period of the trigonometric functions - Read sections 6.3, 6.4 and 6.5
Sketch graph over [0, 2pi)
Domain
Range
Period of the function
Y = sin x
Y = cos x
Y = tan x
Y = cot x
Y = sec x
Y = csc x
17) Period of the trigonometric functions (#11-26, 6.3) – Find exact values without the calculator
a) Sin 405°
b) tan 19pi/6
c) sec 19pi/4
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18) The signs of the trigonometric functions - Name the quadrant in which the angle lies according to certain
given conditions (#27, 34, 6.3)
a) Sinβ > 0, cosβ < 0
b) cosβ > 0, tanβ <0
19) Given a trigonometric function of an angle, and the location of the angle, find the exact
remaining trigonometric functions of the angle
value of the
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20) Even – Odd properties - Which trigonometric functions are
a. Even?
b. Odd
21) Even – odd properties
22) Use identities to find the exact value
o Reciprocal, quotient and Pythagorean identities
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23) Use identities to find the exact value
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