Pre Assessment

• Before you start today’s lesson you must first take the pre assessment by following this link:

• When you have completed the pre assessment you can begin the powerpoint. Have your notebook out, take notes, and make sure you are answering any questions that appear in the powerpoint. I will be checking your notes for a grade at the end of class.

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Trigonometry is derived from Greek words trigonon (three angles) and metron ( measure).

Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees

Triangles on a sphere are also studied, in spherical trigonometry.

Trigonometry specifically deals with the relationships between the sides and the angles of triangles, that is, on the trigonometric functions, and with calculations based on these functions.

Trigonometry

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Right Triangle A triangle in which one angle is

equal to 90 is called right triangle. The side opposite to the right

angle is known as hypotenuse.AB is the hypotenuse

The other two sides are known as legs. When a specific angle is being referenced the legs are called either adjacent or opposite to the angle being referenced.

AC and BC are the legs

Trigonometry deals with Right Triangles

Hyp, Opp, and Adj• In Geometry you learned about three trigonometric

ratios: Sine, Cosine, and Tangent. Before we can go deeper into the study of those ratios we must know the following terminology.

• The hypotenuse (hyp) is the longest side of the triangle – it never changes

• The opposite (opp) is the side directly across from the angle you are considering

• The adjacent (adj) is the side right beside the angle you are considering

Angle in QuestionUse Google to look up the Greek letter theta. Draw theta in your notes and be sure to label the letter theta. Then write one or two sentences about how theta is used in mathematics.

Task 1: Draw the following picture in your notes. Label angle BAC with the theta symbol. If angle BAC is theta,

a. Label the hypotenuseb. Label the opposite legc. Label the adjacent leg

Trigonometric Ratios

Name“say”

Sine Cosine Tangent

AbbreviationAbbrev.

Sin Cos Tan

Ratio of an angle measure

Sinθ = opposite side hypotenuse

cosθ = adjacent side hypotenuse

tanθ =opposite side adjacent side

We can form a total of six ratios using the three any triangle. The first three ratios are below.

Task 2: Make sure you have these ratios in your notes.

hyp

oppsin

hyp

adjcos SOH

adj

opptan

CAHTOA

Sin is Opposite over HypotenuseCos is Adjacent over HypotenuseTan is Opposite over Adjacent

Task 3: Answer the six questions below:

B c a

C b A

1. Write the ratio for sin A

2. Write the ratio for cos A

3. Write the ratio for tan A

#’s 4 – 6: Let’s switch angles: Find the sin, cos and tan for Angle B:

Trigonometric Ratios and Special Right Triangles

Task 4 to be completed in your notes: 1. Draw triangle ABC as a 30° – 60° – 90° triangle.2. Label the hypotenuse 1 unit in length.3. Label the shortest leg as .5 units in length.4. Use the Pythagorean theorem to determine length of the

longest leg.5. Now that you know all the side lengths determine the following:

a. sin(30) = _____ b. cos(30) =_____ c. tan(30) = ____.

Trigonometric Ratios and Special Right Triangles

Task 5 to be completed in your notes: 1. Draw triangle ABC as a 45° – 45° – 90° triangle.2. Label the hypotenuse 1 unit in length.3. Determine the length of the legs and label it in your diagram.4. Now that you know all the side lengths determine the following:

a. sin(45) = _____ b. cos(45) =_____ c. tan(45) = ____.

You have now completed the review of Geometry level Trigonometry.

In Algebra II we will study sine, cosine, tangents and their reciprocals as they relate to a unit circle.

Please raise your hand so that I may check your answers, and give you permission to proceed to the next slides.

Chapter 13 – Trigonometry NotesTask 6: Copy the following definitions into your notes.

Include pictures for reference.

Task 7: Copy the picture of the clock into your notes and answer the questions.

1. In which quadrant does the terminal side of 2:35 lie?

2. Is 3:00 an angle in standard position?

3. Explain why 9:00 is not an angle in standard position using the words terminal side and initial side.

4. What is the positive angle measurement created by the hands of the clock when the clock strikes 3:00pm?

5. What is the negative angle measurement created by the hands of the clock when the clock strikes 3:00pm?

y

x

Measuring AnglesAngles can be measured in two ways:•Degrees•Radians

Degrees…Radians…

Task 8: Determine the angle measure (in degrees) of each angle inside this circle created by the positive x-axis and the various terminal sides. Type your answers in each box provided.

90

60

45

30

0 or 360180

225

300

Angles by Degrees

Task 9:In order to complete the same circle in radian measure, we must first learn what a radian is…

1. Research radians on this website: Make sure you hit the play button if there is one.http://www.mathsisfun.com/geometry/radians.html

2. In your notes record the definition of a radian, and write a few sentences summarizing what you learned from the website.

3. Copy these conversion to notes.

Task 10: Convert all the angles in our previous circle to radian measure. Leave all your answers as fractions with pi in it. NO DECMIALS

π/2

0πAngles in Radians

1.

2.

Read page 830 in your textbook about coterminal angles or research coterminal angles on the internet.

Homework