# Transformations of the Sine and Cosine Graphs

Transformations of the Sine and Cosine Graph – An Exploration By Sharon K. O’Kelley This is an exploration for Advanced Algebra or Precalculus teachers who have introduced their students to the basic sine and cosine graphs and now want their students to explore how changes to the equations affect the graphs. This is an introductory lesson whose purpose is to connect the language of Algebraic transformations to the more advanced topic of trignonometry. (A key follows the end of the exploration.) 1. 2. then the values of a = 1, b = 1, and c = 0. Let’s find out what happens when those values change…. 3. Equation of blue graph Equation of red graph a. b. c. 4. Equation of purple graph Equation of green graph a. b. c. d. 5. b. c. 6. a. b. c. d. 7. a. b. 8. Consider the graph of …. (The first function is in black.) Describe the transformations fully. (Hint: Look at this problem as 9. a. 10. 11. Key to the Exploration 3. a. b. . ) on the red graph. 4. a. b. . c. it is a vertical shrink by . is equivalent to

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Bar modelling- a powerful visual approach for introducing number topics Building on my recent post about a taxonomy for deep learning in maths, I have been trying to think a bit deeper myself about what each type of ‘deep learning link’ might look like. In particular, I have been researching and putting a lot of thought into what effective ‘visual models’ look like for the ‘key nodes’ I have previously identified as the most important foundation maths knowledge for students to master before starting their GCSE maths course. These are principally number topics. Last year I became aware of the Singapore Maths Bar Modelling approached have recently found the time to research it further. I bought some Singapore textbooks and read about the work of Dr Yeap Ban Har. Transformation of Trigonometric Graphs OML Search In these lessons, we will learn how Trigonometric Graphs can be transformed. the amplitude and vertical shift of Trigonometric Graphs the period and phase shift of Trigonometric Graphs Related Topics:More Trigonometric Lessons Stretching and Compressing of Graphs Amplitude of Trigonometric Functions

Radians to degrees How to convert degrees to radians or radians to degrees. Theory: What are 'radians' ? One radian is the angle of an arc created by wrapping the radius of a circle around its circumference. In this diagram, the radius has been wrapped around the circumference to create an angle of 1 radian. Quadratic Functions How can you tell, by LOOKING at a quadratic function, if the vertex is going to be considered 'minimum' or 'maximum' and what exactly is the difference between the two vocabulary words? Well, if you stop and thought about the two words, you just might be able to come up with a logical conclusion. Since a parabola is a U-shape, let's take a look at what this shape looks like in a drawing again and see if you can come up with a conclusion all on your own. Okay, now think of the two words: minimum and maximum. What do they mean? Which of the two parabolas do you think just might indicate minimum and which just might indicate maximum?

Questions on Trigonometric Functions 1. Use the definitions of the six trigonometric functions and the Pythagorean Identity given in the Field Guide Lesson to show that: 1 + tan2(x) = sec2(x) 1 + cot2(x) = csc2(x) Solving Trigonometric Equations Solving Trigonometric Equations (page 1 of 2) Solving trig equations use both the reference angles you've memorized and a lot of the algebra you've learned. Be prepared to need to think! Solve sin(x) + 2 = 3 for 0° < x < 360° Just as with linear equations, I'll first isolate the variable-containing term:

Tricky crocodile maths question befuddles students - but can you answer it? Earlier this year, a maths exam sat by students in Scotland was deemed so difficult that the pass mark had to be lowered. And now, a report has identified the chief culprit - a perplexing question about a crocodile stalking its prey. The pass mark for the new-look Higher maths exam - the Scottish equivalent of an A-level - was slashed to a lowly 34%. According to a report for the Scottish Qualifications Authority (SQA), the action was taken because of the overall difficulty of the test, as opposed to individual questions. However, the report, from the principal assessor in maths, does make specific reference to two questions which sparked outcry among students on social media.

Review : Trig Functions The intent of this section is to remind you of some of the more important (from a Calculus standpoint…) topics from a trig class. One of the most important (but not the first) of these topics will be how to use the unit circle. We will actually leave the most important topic to the next section. First let’s start with the six trig functions and how they relate to each other.

Exploring y=Asin(Bx+C)+D Assignment 1: Exploring Asin(Bx+C)+D by Margo Gonterman Periodic Function A periodic function is a function, such as sin(x), that repeats its values in regular intervals MEI > Teachers > Contextualisation Toolkit Contextualising post-16 GCSE Mathematics: A toolkit for practitioners This resource is designed for teaching practitioners involved in planning and delivering post-16 GCSE Mathematics, including both specialist maths teaching practitioners and vocational teaching practitioners who wish to embed maths in their delivery. The toolkit encourages these practitioners to make greater use of contexts in their delivery of post-16 GCSE Mathematics.

Graphs of trigonometric functions The Topics | Home Zeros of a function The graph of y = sin x The period of a function GCSE, AS and A level Assessment Objectives 1. GCSE assessment objectives Assessment objectives are part of the assessment arrangements for these qualifications. We adopt them into our regulatory framework through the subject-specific conditions that exam boards must comply with when designing their specifications. Jump to:

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