Math 1060 Chapter 2 Note Packet

Math 1060 Chapter 2 Note Packet Name ______

Measuring angles in different units

1 Degrees, Minutes, Seconds

Radian Measure

Right angles Acute angles Obtuse angles

Pairs of complementary angles Pairs of supplementary angles

2 Describe triangle ABC, including measurements of side lengths and angles.

Using A as the point of dilation or vanishing point, dilate the triangle by a scale factor of 3/2. Draw and describe the result.

Using A as the point of dilation, dilate the triangle by a scale factor of 2. Describe your procedure. Draw and describe the result.

3 Standard position of an angle initial ray (side) terminal ray (side)

Coterminal angles

Quadrants

Quadrantal angles

Arc length in radians

HW: 2.1 p.124 #1,9,13,15,35,37,41,45,55,61,65,79

4 Color parallel segments. Color congruent angles.

Q P O N M L K J

A B C D E F G H I

Use a ruler and calculator to determine the following measurements. First measure AB AC AD AE AF AG AH AI

Second measure AJ AK AL AM AN AO AP AQ

first second

How would these values change if we rotated ray AJ counterclockwise? Explain.

Clockwise?

5 Draw an angle in standard position. Make this large enough that you can take notes.

Use a ruler to measure all three sides of your triangle.

6 Color your angle.

Label each side as hypotenuse, adjacent leg, or opposite leg.

Label and set up ratios of sides.

Using the vertex of your angle as the point of dilation, draw a dilated triangle with scale factor 3. Include lengths on each segment.

Label and set up ratios of sides for the dilated triangle.

What is the value of theta?

7 SOH-CAH-TOA

9 10 The County building department has given you a scale drawing of the new ramp to be constructed outside of Farley’s Place. Color the angle of interest. Label the sides as hypotenuse, adjacent leg, opposite leg. Label and set up ratios of sides.

Upon construction at Farley’s Place, the ramp has passed inspection. However, the length of the ramp surface is 4.7 meters. Determine the other dimensions of the ramp.

11 The calculator screen reports that sin17� .292. Explain how this value could be useful.

Use the information below to draw at least two possible triangles. cos60� .5

tan 45� 1

5 Given that theta is acute and cosq = , find tanq . 8

Angle of elevation.

Angle of depression.

12 13 14 Determine the height of the flag pole in front of school (without measuring the height!).

15 Draw an acute angle in standard position. Make this large enough for notes.

Six total trig ratios.

Find six trig ratios for the angle in standard position whose terminal side contains (-3,-2).

16 For each of the following trig ratios, color the quadrants RED whose angles would contain positive values. Color the quadrants BLUE whose angles would have negative values.

Sin cos tan

Csc sec cot

7 If tanq = - and sinq < 0 , find cosq and cscq . 5

Reference Angles

17 Recall your special right triangles.

18 Unit Circle

Do you notice any patterns?

19 Cosx = cos(-x) Even -sinx = sin(-x) Odd

Using the unit circle

20 21 Periodic Functions

Parent graphs for sine function and cosine function

22 Transformations (amplitude and horizontal stretch)

23 Recall the height of the flag pole in the front of school. When the sun is out, the flag pole casts a shadow. Draw a diagram below.

As we move through our planetary rotation, the angle of the sun changes (and so does the length of the shadow). Draw various diagrams to show the flag pole and shadow at different times of the day.

24 Parent graphs of tangent, secant, cosecant, and cotangent functions.

25 Transformations (amplitude and horizontal stretch)

26 Refer to our rabbit and fox population data to respond to the following prompts. What does the length of one cycle appear to be for the rabbit population?

What does the length of one cycle appear to be for the rabbit population?

What is a “y-intercept” or “starting amount” for the rabbit population?

What is a “y-intercept” or “starting amount” for the fox population?

What types of transformations have been made to a parent graph?

How might these changes affect the equations we use to model the data?

27 Graphing ANY trigonometric function using transformations.