By considering the transformation that has taken place, state the coordinates of the first local minimum of each of the given functions for $x\ge0$x≥0.

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The graph $y=\csc x$y=cscx is plotted on a Cartesian plane. One period of $\csc x$cscx is shown from $x=0$x=0 to $x=2\pi$x=2π but the graph extends to the left and right. The first local minimum of $y=\csc x$y=cscx is plotted as a solid dot at $\left(\frac{1}{2\pi},1\right)$(12π,1). The coordinates of the local minimum are not explicitly labeled.

$y=5\csc x$y=5cscx

$y=-5\csc x$y=−5cscx

$y=\csc x+2$y=cscx+2

Easy

4min

Consider the graph of $y=\sec x$y=secx. Its first local minimum for $x\ge0$x≥0 is at $\left(0,1\right)$(0,1).

By considering the transformation that has taken place, state the coordinates of the first local minimum of each of the given functions for $x\ge0$x≥0.

Easy

4min

Determine the equation of the new function after performing the following transformations.

Easy

< 1min

Determine the equation of the new function after performing the following transformations.

Easy

< 1min

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)

Transformations of cot, sec and cosec curves and equations

Interactive practice questions

Outcomes

11.SF.TF.1

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