Trigonometric Graph Worksheet

**Page 1**

1.

Which of the following is a point on the curve $y$ = cot $x$?

a. | ($\frac{\pi}{6}$, $\frac{1}{\sqrt{3}}$) | ||

b. | (0, 0) | ||

c. | ($\frac{\pi}{3}$, $\frac{1}{\sqrt{3}}$) | ||

d. | ($\frac{\pi}{2}$, 1) |

Since

The graph of cot

So, the point (

Correct answer : (3)

2.

The graph of cos $x$

a. | Passes through the origin | ||

b. | Does not pass through ($\frac{\pi}{4}$, 0) | ||

c. | Passes through the point ($\frac{\pi}{2}$, 1) | ||

d. | Does not pass through the origin |

Since

cos

So, graph of cos

Correct answer : (4)

3.

Which of the following is a point on the curve $y$ = tan $x$?

a. | (0, 1) | ||

b. | (- $\frac{\pi}{2}$, 1) | ||

c. | ($\frac{\pi}{2}$, 1) | ||

d. | ($\frac{\pi}{4}$, 1) |

Since

The curve passes through (0, 0), (

So, (

Correct answer : (4)

4.

Through which of the following points does the graph of sin $x$ pass?

a. | ($\frac{\pi}{6}$, $\frac{\sqrt{3}}{2}$) | ||

b. | ($\frac{\pi}{6}$, $\frac{1}{2}$) | ||

c. | ($\frac{\pi}{2}$, 0) | ||

d. | (0, -1) |

Since

The graph of sin

Correct answer : (2)

5.

Which of the following is correct?

a. | The graph of sin $x$ passes through (0, 0) | ||

b. | The graph of sin $x$ does not pass through the origin. | ||

c. | The graph of sin $x$ does not pass through ($\frac{\pi}{2}$, 1) | ||

d. | The graph of sin $x$ does not pass through (-$\frac{\pi}{2}$, -1) |

Correct answer : (1)

6.

The $y$ - intercept of the graph $y$ = sin $x$ is

a. | -1 | ||

b. | 2 | ||

c. | 1 |

[Substitute

So,

Correct answer : (2)

7.

The zeros of the graph $y$ = cos $x$ are existing at $x$ =

a. | $\frac{n\pi}{2}$ for all integer values of $n$ | ||

b. | $n$π for all integer values of $n$ | ||

c. | (2$n$ + 1) $\frac{\pi}{2}$ for all real values of $n$ | ||

d. | (2$n$ + 1) π for all integer values of $n$ |

The solutions of cos

Correct answer : (2)

8.

The $y$ - intercept of $y$ = tan $x$ is:

a. | 2 | ||

b. | -1 | ||

c. | 1 |

[Substitute

So,

Correct answer : (1)

9.

Write the amplitude of $y$ = 5sin($\frac{x}{4}$).

a. | $\frac{1}{3}$ | ||

b. | 5 | ||

c. | 4 |

[Definition.]

On comparing

So, the amplitude of

Correct answer : (3)

10.

Evaluate: $\underset{x\to 0}{\mathrm{lim}}$ $\frac{46{x}^{2}}{1-\mathrm{cos}6x}$

a. | 23 | ||

b. | $\frac{1}{9}$ | ||

c. | $\frac{23}{9}$ | ||

d. | $\frac{23}{3}$ |

[Undefined at

=

[Use 1 - cos 2

= 23

[Divide both the numerator and the denominator by

= 23

[Use quotient law of limits.]

= 23

[Use

Correct answer : (3)