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First Year Math Trigonometric Functions And Their Graphs Find the periods of the following functions:4. \cot \frac{x}{2}


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Find the periods of the following functions:4. \cot \frac{x}{2}

Q.18 Range of \cot x is equal to(a) R (b) Q (c) Z (d) N
Q.18 Range of  \cot x  is equal to(a)  R (b)  Q (c)  Z (d)  N

Q.18 Range of \cot x is equal to(a) R (b) Q (c) Z (d) N

Q.10 Range of y=\sin x equals(a) -1<y<1 (b) y \geq 1 or y \leq-1 (c) -\infty<y<\infty (d) -1 \leq y \leq 1
Q.10 Range of  y=\sin x  equals(a)  -1<y<1 (b)  y \geq 1  or  y \leq-1 (c)  -\infty<y<\infty (d)  -1 \leq y \leq 1

Q.10 Range of y=\sin x equals(a) -1<y<1 (b) y \geq 1 or y \leq-1 (c) -\infty<y<\infty (d) -1 \leq y \leq 1

Q.21 The period of \sin x is :(a) \frac{\pi}{3} (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) 2 \pi
Q.21 The period of  \sin x  is :(a)  \frac{\pi}{3} (b)  \frac{\pi}{2} (c)  \frac{2 \pi}{3} (d)  2 \pi

Q.21 The period of \sin x is :(a) \frac{\pi}{3} (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) 2 \pi

Q.24 The period of \tan x is(a) \frac{\pi}{3} (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) \pi Falsalabad Board 2013; Lahore Board 2016; 2004
Q.24 The period of  \tan x  is(a)  \frac{\pi}{3} (b)  \frac{\pi}{2} (c)  \frac{2 \pi}{3} (d)  \pi Falsalabad Board 2013; Lahore Board 2016; 2004

Q.24 The period of \tan x is(a) \frac{\pi}{3} (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) \pi Falsalabad Board 2013; Lahore Board 2016; 2004

Q.9 The range of y=\sin x is(a) [-11] (b) [-10] (c) [-22] (d) none of these
Q.9 The range of  y=\sin x  is(a)  [-11] (b)  [-10] (c)  [-22] (d) none of these

Q.9 The range of y=\sin x is(a) [-11] (b) [-10] (c) [-22] (d) none of these

Q.29 The period of \sin \frac{x}{2} is(a) 2 \pi (b) 4 \pi (c) \pi (d) none
Q.29 The period of  \sin \frac{x}{2}  is(a)  2 \pi (b)  4 \pi (c)  \pi (d) none

Q.29 The period of \sin \frac{x}{2} is(a) 2 \pi (b) 4 \pi (c) \pi (d) none

Q.1 Domain of y=\cos x is :(a) -\infty<x<+\infty \begin{array}{ll}\text { (b) }-1 \leq y \leq 1 & \text { (c) } 0<x<\infty\end{array} (d) -\infty<x<0
Q.1 Domain of  y=\cos x  is :(a)  -\infty<x<+\infty  \begin{array}{ll}\text { (b) }-1 \leq y \leq 1 & \text { (c) } 0<x<\infty\end{array} (d)  -\infty<x<0

Q.1 Domain of y=\cos x is :(a) -\infty<x<+\infty \begin{array}{ll}\text { (b) }-1 \leq y \leq 1 & \text { (c) } 0<x<\infty\end{array} (d) -\infty<x<0

Q.34 Period of \sin \frac{x}{3} is(a) \pi (b) 3 \pi (c) \frac{2 \pi}{3} (d) 6 \pi Lahore Board 2014
Q.34 Period of  \sin \frac{x}{3}  is(a)  \pi (b)  3 \pi (c)  \frac{2 \pi}{3} (d)  6 \pi Lahore Board 2014

Q.34 Period of \sin \frac{x}{3} is(a) \pi (b) 3 \pi (c) \frac{2 \pi}{3} (d) 6 \pi Lahore Board 2014

Q.26 The period of \sin 2 x is(a) \frac{\pi}{3}= (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) \pi
Q.26 The period of  \sin 2 x  is(a)  \frac{\pi}{3}= (b)  \frac{\pi}{2} (c)  \frac{2 \pi}{3} (d)  \pi

Q.26 The period of \sin 2 x is(a) \frac{\pi}{3}= (b) \frac{\pi}{2} (c) \frac{2 \pi}{3} (d) \pi

Find the periods of the following functions:8. \cos \frac{x}{6}
Find the periods of the following functions:8.  \cos \frac{x}{6}

Find the periods of the following functions:8. \cos \frac{x}{6}

Q.35 The period of \cos \frac{x}{5} is :(a) 10 \pi (b) \frac{2 \pi}{5} (c) 2 \pi (d) none of theseGujranwala Board 2006
Q.35 The period of  \cos \frac{x}{5}  is :(a)  10 \pi (b)  \frac{2 \pi}{5} (c)  2 \pi (d) none of theseGujranwala Board 2006

Q.35 The period of \cos \frac{x}{5} is :(a) 10 \pi (b) \frac{2 \pi}{5} (c) 2 \pi (d) none of theseGujranwala Board 2006

Q.6 The domain of \cot x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\} Lahore Board 2010
Q.6 The domain of  \cot x  is(a)  [-11] (b)  R (c)  R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d)  R-\{x \mid x=n \pi n \in Z\} Lahore Board 2010

Q.6 The domain of \cot x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\} Lahore Board 2010

Find the periods of the following functions:9. \tan \frac{x}{7}
Find the periods of the following functions:9.  \tan \frac{x}{7}

Find the periods of the following functions:9. \tan \frac{x}{7}

Find the periods of the following functions:2. \cos 2 x
Find the periods of the following functions:2.  \cos 2 x

Find the periods of the following functions:2. \cos 2 x

Q.12 The range of \tan x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}
Q.12 The range of  \tan x  is(a)  [-11] (b)  R (c)  R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d)  R-\{x \mid x=n \pi n \in Z\}

Q.12 The range of \tan x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}

Find the periods of the following functions:3. \tan 4 x
Find the periods of the following functions:3.  \tan 4 x

Find the periods of the following functions:3. \tan 4 x

1. Draw the graph of each of the following function for the interals mentioned agaiss.
1. Draw the graph of each of the following function for the interals mentioned agaiss.

1. Draw the graph of each of the following function for the interals mentioned agaiss.

Find the periods of the following functions:5. \sin \frac{x}{3}
Find the periods of the following functions:5.  \sin \frac{x}{3}

Find the periods of the following functions:5. \sin \frac{x}{3}

Q.30 Period of \sin \frac{x}{5} is :(a) 2 \pi (b) \frac{\pi}{5} (c) 10 \pi (d) 5 \pi Gujranwala Board 2013
Q.30 Period of  \sin \frac{x}{5}  is :(a)  2 \pi (b)  \frac{\pi}{5} (c)  10 \pi (d)  5 \pi Gujranwala Board 2013
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Q.30 Period of \sin \frac{x}{5} is :(a) 2 \pi (b) \frac{\pi}{5} (c) 10 \pi (d) 5 \pi Gujranwala Board 2013

Q.17 Domain of \cos x is(a) Z (b) Q (c) R (d) none of these
Q.17 Domain of  \cos x  is(a)  Z (b)  Q (c)  R (d) none of these
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Q.17 Domain of \cos x is(a) Z (b) Q (c) R (d) none of these

Q.7 The domain of \sec x is(a) [-11] (b) R (c) R=\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}
Q.7 The domain of  \sec x  is(a)  [-11] (b)  R (c)  R=\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d)  R-\{x \mid x=n \pi n \in Z\}
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Q.7 The domain of \sec x is(a) [-11] (b) R (c) R=\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}

Find the periods of the following functions:4. \cot \frac{x}{2}
Find the periods of the following functions:4.  \cot \frac{x}{2}
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Find the periods of the following functions:4. \cot \frac{x}{2}

Q.32 The period of 3 \sin \frac{x}{3} is(a) \pi (b) 2 \pi (c) 3 \pi (d) 6 \pi
Q.32 The period of  3 \sin \frac{x}{3}  is(a)  \pi (b)  2 \pi (c)  3 \pi (d)  6 \pi
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Q.32 The period of 3 \sin \frac{x}{3} is(a) \pi (b) 2 \pi (c) 3 \pi (d) 6 \pi

Q.22 Period of sine function is(a) \pi \begin{array}{ll}\text { (b) }-\pi & \text { (c) } 2 \pi\end{array} (d) 0
Q.22 Period of sine function is(a)  \pi  \begin{array}{ll}\text { (b) }-\pi & \text { (c) } 2 \pi\end{array} (d) 0
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Q.22 Period of sine function is(a) \pi \begin{array}{ll}\text { (b) }-\pi & \text { (c) } 2 \pi\end{array} (d) 0

Q.2 The range of y=\cos x is : \begin{array}{llll}\text { (a) }-1 \leq x \leq 1 & \text { (b) }-\infty<x<+\infty & \text { (c) }-1 \leq y \leq 1 & \text { (d) }-\infty<y<+\infty\end{array} Lahore Board 2010
Q.2 The range of  y=\cos x  is : \begin{array}{llll}\text { (a) }-1 \leq x \leq 1 & \text { (b) }-\infty<x<+\infty & \text { (c) }-1 \leq y \leq 1 & \text { (d) }-\infty<y<+\infty\end{array} Lahore Board 2010
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Q.2 The range of y=\cos x is : \begin{array}{llll}\text { (a) }-1 \leq x \leq 1 & \text { (b) }-\infty<x<+\infty & \text { (c) }-1 \leq y \leq 1 & \text { (d) }-\infty<y<+\infty\end{array} Lahore Board 2010

Q.11 The range of \cos x is(a) [01] (b) R (c) [-11] (d) [-10]
Q.11 The range of  \cos x  is(a)  [01] (b)  R (c)  [-11] (d)  [-10]
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Q.11 The range of \cos x is(a) [01] (b) R (c) [-11] (d) [-10]

Q.23 The period of \cos x is(a) \pi (b) 2 \pi (c) 3 \pi (d) 4 \pi
Q.23 The period of  \cos x  is(a)  \pi (b)  2 \pi (c)  3 \pi (d)  4 \pi
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Q.23 The period of \cos x is(a) \pi (b) 2 \pi (c) 3 \pi (d) 4 \pi

Q.5 The domain of \tan x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}
Q.5 The domain of  \tan x  is(a)  [-11] (b)  R (c)  R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d)  R-\{x \mid x=n \pi n \in Z\}
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Q.5 The domain of \tan x is(a) [-11] (b) R (c) R-\left\{x \mid x=(2 n+1) \frac{\pi}{2} n \in Z\right\} (d) R-\{x \mid x=n \pi n \in Z\}

Q.28 The period of 3 \cos 2 x is(a) \pi (b) 2 \pi (c) 3 \pi (d) \frac{\pi}{2}
Q.28 The period of  3 \cos 2 x  is(a)  \pi (b)  2 \pi (c)  3 \pi (d)  \frac{\pi}{2}
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Q.28 The period of 3 \cos 2 x is(a) \pi (b) 2 \pi (c) 3 \pi (d) \frac{\pi}{2}

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