Graphing trig functions: sec, scs, cot Quiz 1

Question 1

Given that the amplitude of a cosecant trigonometric function is 5 while the phase shift of the function is 1 radian, find the value of the vertical shift such that the aforementioned function has the same absolute minimum as $$g=\csc (x)$$ for $$g\ge 0$$.

Accepted Answer

$$4$$

Answer

$$2$$

Answer

$$1$$

Answer

$$3$$

Question 2

A wave is transmitted through the vacuum. The function of the wave is calculated to be $$f(x)=3\sin 2x$$ for a time period. For what value or values of $$x$$ does $$f(x)$$ have a relative maximum?

Accepted Answer

$$\dfrac{\pi }{4}$$

Answer

$$\dfrac{\pi }{3},\dfrac{\pi }{4}$$

Answer

$$\dfrac{\pi }{2}$$

Answer

$$\dfrac{\pi }{6},\dfrac{\pi }{4},\dfrac{\pi }{3}$$

Question 3

A student was asked to graph the function of  $$\dfrac{1}{3}\cot \left( \dfrac{1}{2}x \right)$$ . Given that the teacher asked the student to graph the function in the interval $$[0,3\pi ]$$, calculate the $$x-$$intercepts of the function.

Accepted Answer

$$x=\pi ,3\pi $$

Answer

$$x=\pi ,2\pi $$

Answer

$$x=2\pi ,3\pi $$

Answer

$$x=1.061,7.344$$

Question 4

For a function $$\sec (x-1)+1$$ with $$y\ge 0$$, a new secant function has twice the amplitude, the frequency is twice as well as a vertical shift of 3 units more that of the previous function. Calculate the possible horizontal shift.

Accepted Answer

$$0.5$$units

Answer

$$1$$unit

Answer

$$1.5$$units

Answer

$$3$$units

Question 5

Identify the below function a student drew. <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/1f794aa9-a4e5-4f34-b715-f8cbfa85592e5908558311198762636.png"/>

Accepted Answer

$$f(x)=\sqrt{3}\cot \left( 2x-\dfrac{5\pi }{2} \right)+1$$

Answer

$$f(x)=\dfrac{1}{\sqrt{3}}\cot \left( 2x-\dfrac{5\pi }{2} \right)+1$$

Answer

$$f(x)=\sin (\cos (x))$$

Answer

$$f(x)=3	an \left( 2x-\dfrac{5\pi }{2} ight)+1$$