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.

2  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

3 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 Question Use 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 hypotenuse b.Label the opposite leg c.Label the adjacent leg

Trigonometric Ratios Name “say” SineCosineTangent Abbreviatio n Abbrev. SinCosTan 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. SOHCAHTOA Sin is Opposite over HypotenuseCos is Adjacent over Hypotenuse Tan 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 Notes Task 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 Angles Angles 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 or

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. 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 0π

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