Geometry

Graphs of Trigonometric Functions

Trigonometric Graphs - Amplitude and Periodicity

Consider two functions f ( x ) = 25 sin 6 x , g ( x ) = x 2 . f(x)=25-\sin 6x, g(x)=\left\lfloor \frac{x}{2} \right\rfloor. 找到之和of all the elements in the range of g ( f ( x ) ) g(f(x)) .

Details and assumptions

The function x : R Z \lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z} refers to the greatest integer smaller than or equal to x x . For example, 2.3 = 2 \lfloor 2.3 \rfloor = 2 and 5 = 5 \lfloor -5 \rfloor = -5 .

If the period of the function f ( x ) = 224 + cos x + 226 cos x f(x)=\sqrt{224+\cos x}+\sqrt{226-\cos x} is a a , what is the value of f ( a ) f(a) ?

Consider two functions f ( x ) = 7 sin x + 12 , g ( x ) = π cos π x . f(x)=7\sin x+12, g(x)=\pi\cos \pi x. If a a and b b are the maximum and minimum values, respectively, of f ( g ( x ) ) f(g(x)) , what is a + b a+b ?

The graph of y = 7 tan ( 2 π x π ) + 18 y=7 \tan (2\pi x-\pi)+18 has period 1 a \frac{1}{a} . What is the value of a a ?

What is the sum of the maximum and minimum values of the function y = sin x 7 + 20 ? y=|\sin x-7|+20?

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