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Use properties of similar triangles to explain sine, cosine, and tangent Define sine, cosine, and tangent in terms of ratios Explain how trigonometric ratios and relationships help in solving problems Use trigonometric relationships to solve real world problems ο§ Using right triangles Translate trigonometric functions to represent a scenario Relate sine and cosine by explaining their relationship with: right triangles, unit circle, sine/cosine waves Explain π ππ2 π + πππ 2 π = 1 using Pythagorean Theorem and the unit circle ο§ Angles of elevation and depression ο§ Sine and Cosine waves Write a sine value in terms of cosine and vice versa SIMILAR TRIANGLES ACTIVITY Learning Target: Use properties of similar triangles to explain sine, cosine, and tangent Discovering Trigonometry β Class Activity WRAP UP: reflect on the learning target in your own words TRIGONOMETRIC RATIOS Learning Target: Define sine, cosine, and tangent in terms of ratios Ratio table What are some possible applications of this tool? WRAP UP: What are sine, cosine, and tangent? Create a triangle and describe where you can βseeβ these relationships. UNIT ASSESSMENT ESSAY QUESTION #1 1. Explain how sine, cosine, and tangent relate to similar triangles. Use diagrams, tables, numbers, and words to justify your reasoning. APPLICATIONS Learning Targets: Use trigonometric relationships to solve real world problems ο§ Using right triangles ο§ Angles of elevation and depression PRACTICE APPLYING TRIGONOMETRY Please complete this for class tomorrow Practice 1 (No context) Practice 2 (with context) ANGLE OF THE SUN TASK PAPER REQUIREMENTS 1. Hypothesis 2. Methods 3. Diagrams and angles 4. Minimum of 2 graphs + analysis of each 1.Time vs angle 2.Time vs shodow 5. Sources of error in results 6. Conclusions OVERLAPPING CIRCLES PRE-TASK FOR 1ST SUMMATIVE SETTING UP SPRINKLERS Summative Task (can be worked on collaboratively, must be turned in individually) UNIT ASSESSMENT - ESSAY QUESTION #2 2. Define sine, cosine, and tangent and explain how trigonometric ratios help in solving problems. Provide examples of being given two sides versus given a side and an angle. Use diagrams, tables, numbers, and words to justify your reasoning. DOMINGOβS RIDE DOMINGO GETS ON AT POINT A Domingo rides the Ferris wheel at the fair. It has a radius of 36 feet. When Domingo gets on the Ferris wheel it is 4 feet above the ground. How far above the ground is Domingo at each point on the Ferris wheel? CREATE A GRAPH THAT DESCRIBES DOMINGOβS PATH What relationships are noticeable here? What connections can you make between the unit circle and the ratios on the trig table? Sine and Cosine waves as related to the unit circle Learning Target: Understand Sine and Cosine waves as a function Learning Target: Relate sine and cosine by explaining their relationship with: right triangles, unit circle, sine/cosine waves Get out 2 pieces of graph paper, your unit circle, and your trig table Each page needs to be horizontal Scale your x βaxis from zero to 360 degrees. Scale your y β axis from -1 to 1 (use a small increment, around .1) Plot the graph of the sine ratios from zero degrees to 360 degrees on one page and plot cosine graph on the other. Sine Wave Video WRAP UP: Reflect on the relationships on the sine and cosine graph and the relationships between them. TRANSLATE COS(π) INTO THE FOLLOWING f(x) = - cos(π) f(x) = cos(-π) f(x) = cos(ππ) f(x) = cos(π/2) f(x) = 5cos(π) f(x) = cos(π) +10 f(x) = - cos(π - 90) Please use a graphing calculator or desmos.com to graph and compare these translations of cosine When the term inside the brackets gets divided by 2 the cosine wave gets stretched by a factor of two. I can generalize that the divisor when inside the brackets will stretch my wave by the factor it divides by. GRAPHING SINE AND COSINE Can you write a function that represents Domingoβs place on the wheel as a function of time? Use sin or cosine (x) - not both, then translate your equation to fit the graph. HOW CAN WE SEE THIS IDENTITY REPRESENTED IN Aβ¦? Learning Target: Explain π ππ2 π + πππ 2 π = 1 using Pythagorean Theorem and the unit circle β’ β’ β’ β’ Unit Circle Sine and Cosine waves Right Triangles Trig Table Wrap up: Note the places and ways we can see the trig identity π ππ2 π + πππ 2 π = 1 in each representation. UNIT ASSESSMENT β ESSAY #3 3. Explain the relationship between sine and cosine. How does the unit circle show the relationship? How do the sine and cosine wave show the relationship? How can the sine of an angle be related to the cosine of an angle? How is the trigonometric identity ππππ π + ππππ π = π related to different representations? Use diagrams, tables, numbers, and words to justify your reasoning. SINE AND COSINE COMPLEMENTS POWERPOINT UH β OH! I NEED TO REASSESS, NOW WHAT? Complete the following practices prior to reassessing β all work must be shown 1. Finding sides using trig - Practice 2. Finding angles using inverse trig functions β Practice 3. What is the unit circle β Watch video and write a reflection. 4. How are similar triangles related to trigonometry β Watch video and write reflection 5. How can I use trig functions to solve problems - Watch video and write reflection