What is the period of the function $$y=2\text{sec}igg(\frac{1}{2}xigg)-1$$ ?

The period of the function $$y=2\text{sec}igg(\frac{1}{2}xigg)-1$$ is $$4\text{π}$$ .

What is the range of the cosecant function, $$y=\text{csc} x$$ ?

The range of the cosecant function is $$(-\text{∞}, -1] igcup [1, \text{∞})$$ .

What is the domain of the function $$y=-7\text{cos}(3x+\frac{2\text{π}}{3})-2$$ ?

The domain of the function is $$(-\text{∞}, \text{∞})$$ , meaning it is defined for all real numbers.

How do you find the period of the function $$y=\text{tan}(kx)$$ ?

The period of the function is given by $$\frac{\text{π}}{k}$$ , where k is the coefficient of x.

What is the vertical shift in the function $$y=\text{sin}(x)+2$$ ?

The vertical shift is 2 units upward, as indicated by the +2.

What is the phase shift of the function $$y=\text{cos}(x-\frac{\text{π}}{4})$$ ?

The phase shift is $$\frac{\text{π}}{4}$$ units to the right.

What is the relationship between the sine and cosine functions?

The sine and cosine functions are related by the identity $$\text{sin}^2(x) + \text{cos}^2(x) = 1$$ .

What is the effect of changing the coefficient of x in $$y=\text{sin}(kx)$$ ?

Changing the coefficient k affects the period of the sine function, making it shorter for larger k and longer for smaller k.

What is the maximum value of the function $$y=5\text{cos}(x)$$ ?

The maximum value of the function is 5, which is the coefficient of the cosine function.

What is the definition of the secant function, sec x?

The secant function is the reciprocal of the cosine function, defined as sec x = 1/cos x. It is undefined where cos x = 0.

What is the effect of a negative coefficient in front of the cosine function?

A negative coefficient reflects the graph of the cosine function over the x-axis.

What is the range of the sine function, $$y=\text{sin}(x)$$ ?

The range of the sine function is $$[-1, 1]$$ .

Graphs of Trigonometric Functions

Flashcard

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Mathematics

•

11th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF-IF.C.7E, HSF.TF.A.2, HSF.TF.C.8

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FLASHCARD QUESTION

Front

What is the cosecant function, csc x?

Back

The cosecant function is the reciprocal of the sine function, defined as csc x = 1/sin x. It is undefined where sin x = 0.

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