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India
Class XI

Domain and range of cot, sec and cosec curves

Interactive practice questions

Consider the function $f\left(x\right)=\csc x$f(x)=cscx, which is defined as the reciprocal function of $\sin x$sinx. That is, $\csc x=\frac{1}{\sin x}$cscx=1sinx.

a

Which of the following describes the values of $x$x where $\sin x=0$sinx=0?

$x=\pi n+\frac{\pi}{2}$x=πn+π2 where $n$n is an integer.

A

$x=2\pi n$x=2πn where $n$n is an integer.

B

$x=\pi n$x=πn where $n$n is an integer.

C

$x=\frac{\pi}{2}n$x=π2n where $n$n is an integer.

D
b

What does your answer to part (a) imply about the function $f\left(x\right)=\csc x$f(x)=cscx?

$f\left(x\right)$f(x) is undefined when $x=\pi n$x=πn.

A

$f\left(x\right)$f(x) will reach its maximum value when $x=\pi n$x=πn.

B

$f\left(x\right)=0$f(x)=0 when $x=\pi n$x=πn.

C

$f\left(x\right)$f(x) will reach its minimum value when $x=\pi n$x=πn.

D
Easy
1min

Consider the function $f\left(x\right)=\sec x$f(x)=secx, which is defined as the reciprocal function of $\cos x$cosx. That is, $\sec x=\frac{1}{\cos x}$secx=1cosx.

Easy
1min

Consider the function $f\left(x\right)=\cot x$f(x)=cotx, which is defined as the reciprocal function of $\tan x$tanx. That is, $\cot x=\frac{1}{\tan x}$cotx=1tanx.

Easy
1min

Consider the function $f\left(x\right)=\sec x$f(x)=secx, which is defined as the reciprocal function of $\cos x$cosx. That is, $\sec x=\frac{1}{\cos x}$secx=1cosx.

Easy
1min
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Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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