MHF4U NAME: ________________________ DATE: _____________

6.1-6.4 CLASS NOTES

6.1 – Radian Measure

Angles can be measured in Degrees, Revolutions & Radians.

Radian Measure:The size of an angle is expressed in terms of the length of an arc, a, that subtends (“joins the ends of”) the angle θ, at the center of a circle with radius r.

Recall: The arc length created by a 360 ° angle will be equal to the circumference of a circle.

Recall: the formula of the circumference of a circle: _________________.

Let’s figure out the radian measure (θ ¿ of a full circle!

Therefore, the radian measure of a full circle is:

_____________

PRACTICE EXAMPLE 1: Starting at 0 ° , draw a diagram to represent each radian measure.

PRACTICE EXAMPLE 2: Convert the following into radian measures.

PRACTICE EXAMPLE 3: Convert the following into degree measures:

6.1 Homework: P. 320 #1-4, 7-8

6.2 – Radian Measure & Angles on the Cartesian Plane

Recall: Special Triangles & Cartesian Plane! Determine the length of the missing sides and the radian measures for the angles.

Determine the EXACT value of each Trig Ratio:

Radians

Degrees

0 π6

π4

π3

π2

π 3π2

2π

sin θ

cosθ

tanθ

csc θ

secθ

cot θ

Recall: Cartesian Grid & C.A.S.T. Rule

PRACTICE EXAMPLE 1: State an equivalent expression in terms of the RAA.

Helpful Hints:

1) Determine which quadrant the terminal arm is in. Recall that π=180 ° 2) The RAA is ALWAYS “attached” to the x-axis. Never the y-axis.

PRACTICE EXAMPLE 2: Evaluate using the related angle identities; Give exact values!

PRACTICE EXAMPLE 3: Determine the exact value for the following:

PRACTICE EXAMPLE 4: Determine the exact value for the following:

PRACTICE EXAMPLE 5:

6.2 Homework: P. 330 #1acd, 2ac, 3-7, 9, 11, 13, 15

6.3 – Sketching the Base Graphs of Trigonometric FunctionsComplete the table of values for 0≤ x≤2π and sketch the graph of the functions.

y=sin xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

y=cos xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

y=tan xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

y=csc xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

y=sec xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

y=cot xValue of x(radians)

0 π6

π3

π2

2π3

5π6

π 7π6

4 π3

3π2

5π3

11π6

2π

Value of x(degrees)

Exact Value

Decimal Value

Complete the following chart that summarizes the characteristics of the primary and reciprocal trigonometric functions.

Characteristic y=sin x y=cos x y=tan x y=csc x y=sec x y=cot x

Domain

Range

Maximum Value

Minimum Value

Amplitude

Axis

Period

x - intercepts

y - intercepts

6.3 HOMEWORK: P. 349 #1-6

6.4 – Sketching the Base Graphs of Trigonometric Functions

8.4 HOMEWORK: P. 343 #1, 4-6