MATH 165 – Chapter 6 - TOPICS and practice – Use a basic calculator unless indicated otherwise

Section 6.1 – Angles and their measures

1) Vocabulary Angle:

o Initial Sideo Terminal Sideo Vertex

Positive angle (counterclockwise rotation) Negative angle (clockwise rotation) Standard position of an angle

Angle that lies in a quadrant Quadrantal angle Central Angle

Units of measurement of angles:o Degreeso Radians

2) Relationships between degrees, minutes and seconds

a) Convert an angle from degrees to degrees, minutes and secondsi) 35.76 degrees to DMS -

b) Convert an angle from degrees, minutes and seconds to degreesi) 56 º 35’ 40” to Degrees -

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Section 6.1 – Angles and their measures

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 – Trigonometric Functions

4) The six trigonometric functions: triangle approach

5) The six trigonometric functions: unit circle approach

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Section 6.2 – Trigonometric Functions

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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Section 6.2 – Trigonometric Functions

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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Section 6.2 – Trigonometric Functions

13) Trigonometric functions: FUNCTION NOTATION:

14) Trig – function notation - operations

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Section 6.2 – Trigonometric Functions

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 6.5Sketch 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 calculatora) Sin 405° b) tan 19pi/6 c) sec 19pi/4

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Section 6.3 – Properties of Trigonometric Functions

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 value of the remaining trigonometric functions of the angle

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Section 6.3 – Properties of Trigonometric Functions

20) Even – Odd properties - Which trigonometric functions are a. Even? b. Odd

21) Even – odd properties

22) Identities - Write the reciprocal, quotient and Pythagorean identities

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Section 6.3 – Properties of Trigonometric Functions

23) Use identities to find the exact value

24) Use identities to find the exact value

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Section 6.3 – Properties of Trigonometric Functions

25) Solve the problem

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