Graphs of Trigonometric Functions

Concept Quizzes

Graphs of Trigonometric Functions Warmup
Sine and Cosine Graphs
Tangent and Cotangent Graphs
Cosec and Sec Graphs
Inverse Trigonometric Graphs
Symmetry in Trigonometric Graphs
Trigonometric Graphs - Amplitude and Periodicity
Graphical Transformation of Trigonometric Functions
Recognizing Trigonometric Graphs
Graphs of Trigonometric Functions - Problem Solving

Challenge Quizzes

Graphs of Trigonometric Functions: Level 2 Challenges
Graphs of Trigonometric Functions: Level 3 Challenges

Graphs of Trigonometric Functions Warmup

If the graph in red is $y = 3\sin(x)$ , what could the graph in blue be?

y = -1.6 \sin(x)

y = 4.4 \sin (x)

y = 1.6 \sin (x)

y = -4.4 \sin (x)

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by Brilliant Staff

What's the minimum possible value of $y$ for

$y = -5 \sin(2x - \pi) - 2 ?$

-5+\pi

-5

-3

-7

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by Brilliant Staff

The $\arccos$ function is typically defined by taking the inverse of a cosine with a domain of $[0, \pi)$ . What would be the effect if the inverse was of a cosine with a domain of $[0, 2\pi)$ instead? (The graphs below may help.)

Graph of $f(x) = \cos(x)$ :

Graph of $f(x) = \arccos(x)$ :

The arccosine would no longer be a function There would be a possible division by zero There would be inputs to the function with no output

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by Brilliant Staff

The interval depicted is 0 to $4 \pi$ . Which of these could not represent the graph above?

y=\csc(x)

y=\sec(x-\frac{\pi}{2})

y=\csc(x+2\pi)

y=\sec(x+\pi)

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by Brilliant Staff

Starting from the basic definition of the tangent function, which is these facts most directly implies the tangent graph has a vertical asymptote at $\frac{\pi}{2}$ ?

\cos(\frac{\pi}{2}) = 0

\tan(\frac{\pi}{4}) = 1

\sin(\frac{\pi}{2}) = 1

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by Brilliant Staff