Presentation on theme: "Welcome to Trigonometry!"— Presentation transcript:
1Welcome to Trigonometry! We’ll be “Getting’ Triggy” with these concepts…6.1: find exact values of trigonometric functions (5-1)6.2: find coterminal and reference angles and to covert between units of angle measure (5-1)6.3: solve for missing values in right triangles (5-4, 5-5)6.4: use the law of sines and cosines and corresponding area formulas (5-6)6.5: use the ambiguous case of the law of sines to solve problems (5-7)
3In this section we will answer… 6.2 find coterminal and reference angles and to convert between units of angle measure (5-1)In this section we will answer…How are angles measured in Trig?What are the different units of angle measure within degree measurement?What does it mean for angles to be co-terminal?How can I find a reference angle?
5In Trig Angles are always placed on the coordinate plane. The vertex is at the origin and one side (the initial side) lies along the x-axis.The other side (the terminal side) lies in a quadrant or on another axii.This is called Standard Position.
6Angle Direction: Angles can be measured in two directions. Counter-clockwise is positive.Clockwise is negative.
7Degree Measurement: One full rotation = _________________. The circle has been cut into 360 equal pieces.Measure of less than a degree can be shown 2 ways:Decimal pieces: ºMinutes and seconds: used for maps 103º 45’ 5”Each degree is divided into 60 minutes.Each minute is divided into 60 seconds.1º = 60’ = 3600”
236.3: solve for missing values in right triangles (5-4, 5-5) In these sections we will answer…How are the 6 trig ratios expressed in geometry? In trig?How can I use these relationships to solve triangle problems?
24Right Triangles in Geometry: ∆ ABCUsed the 3 basic trig ratios:sin A, cos A and tan A.SOH-CAH-TOANow we will add 3 reciprocal ratios:csc A, sec A and cot A.
376.1: find exact values of trigonometric functions (5-2/5-3) In this standard we will…Review the side relationships of 30°-60°-90° and 45°-45°-90° triangles.Build trig ratios based 30°-60°-90° and 45°-45°-90° triangles.
38Special Triangles from Geometry: Build a chart to show all 6 trig ratios.
44The apothem of a regular pentagon is 10.8 cm. Answer the following. Find the radius of the circumscribed circle.What is the length of one side of the pentagon?Find the perimeter of the pentagon.ra = 10.8 cm
45p 303Mr. Fleming is flying a kite. Ms Case notices the string makes a 70˚ angle with the ground. “I know the string is 65 meters long,” says Ms Case. “I wonder how far is the kite above the ground?”Ranger Gladd sights a fire from his fire tower in Alvarez National forest. He finds an angle of depression to the fire of 22˚. If the tower is 75 meters tall, how far is the fire from the base of the tower?
46Partner Solve: ONE piece of paper. One person solves then second person checks and either praises or coaches.Change jobs.Do p 301 #1 – 9 all
47Homework:LEARN YOUR SPECIAL TRIANGLES or UNIT CIRCLE!P 303 #11-29 odd
52Inverse/arc trig ratios: To show you want to inverse or “undo” a trig ratio in order to get an angle there are two notations:
53Evaluate each expression assuming a Quadrant I angle.
54Architecture:Many cities place restrictions on the height and placement of skyscrapers in order to protect residents from completely shaded streets. If a 100-foot building casts an 88-foot shadow, what is the angle of elevation to the sun?
55Partner Workout! P 309 #1 –14 all One piece of paper, take turns solving.If you aren’t solving you are the cheerleader/spotter. Encourage and save them from falling on their face.
56Homework: LEARN YOUR SPECIAL TRIANGLES or UNIT CIRCLE! P309 #15 – 45 odd
74Section 5-7: The Ambiguous Case for the Law of Sines In this section we will answer…When can I use Law of Sines?Is there ever a case where ASS actually WORKS?How can I determine when I can use this really inappropriate acronym?Do I have to memorize the chart?
75When can I use Law of Sines? If I have…AAS or ASA, always works!SAS or SSS, never works!
76Is there ever a case where ASS actually WORKS? Exploration:
77Our Nifty, Triangle Info Sheet! Do I have to memorize the chart?