5.1 & 5.3: Graphs and Transformations of the Primary Trig Functions
- The graphs of y = sinx, y = cosx, and y = tanx are periodic
- The graphs of y = sinx, y = cosx are similar in shape and have an amplitude of 1 and a period of (2pi)
- The graph of y = tanx has no amplitude because it has no maximum or minimum values. It is undefined at values of x that are odd multiples of pi/2. The graph becomes asymptotic as the angle approaches these values from the left and the right. the period of the function is pi.
- The transformation of a sine or cosine function f(x) to g(x) has the general form g(x) = a f [k(x - d)]+c, where a is the amplitude, d is the phase shift, and c is the vertical translation
- The period of the transformed function is given by (2pi/k)
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5.2: Graphs of Reciprocal Trigonometric Functions
- The graphs of y = cscx, y = secx, and y = cotx are periodic. They are related to the graphs of the primary trigonometric functions as reciprocal graphs.
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5.4: Solve Trigonometric Equations
- Trigonometric equations can be solved algebraically by hand or graphically with technology.
- There are often multiple solutions. Ensure that you find all solutions that lie in the domain of interest
- Quadratic trigonometric equations can often be solved by factoring.
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5.4_numbers_4_6_and_9.pdf | |
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5.5: Making Connections and Instantaneous Rates of Change
- The instantaneous rates of change of a sinusoidal function follow a sinusoidal pattern
- Many real-world processes can be modelled with a sinusoidal function, even if they do not involve angles
- Modelling real-world processes usually requires transformations of the basic sinusoidal functions.
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determining_the_equations_of_sinusoidal_functions.pdf | |
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graphing_and_modelling_with_trig_functions.pdf | |
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