Sine, cosine, tangent and cotangent

2010016408

Level: 
B
Consider the function \(f(x)=\mathop{\mathrm{cotg}}\nolimits x\) with domain restricted to the interval \( (0;\pi )\). In the following list identify the function with domain \(\left (0; \frac{\pi } {2}\right )\).
\(f(2\cdot x)\)
\(f(x+2)\)
\(f(x-2)\)
\(f(\frac{x}2)\)

2010016407

Level: 
B
Identify the transformation which transforms the graph of the function \(g(x) =\cos (2x)\) to the graph of the function \(f(x) =\cos (2x -1)\).
Shift of graph of \(g\) by \(\frac{1} {2}\) of a unit to the right.
Shift of graph of \(g\) by \(\frac{1} {2}\) of a unit to the left.
Shift of graph of \(g\) by \(1\) unit to the left.
Shift of graph of \(g\) by \(1\) unit to the right.

2010016406

Level: 
B
In the following list identify a true statement about the function \(f(x) =\sin x\) on the interval \(I=\left( -\frac{\pi }{2}; \frac{\pi } {2} \right) \).
The function \(f\) does not have a minimum or maximum on \(I\).
The function \(f\) has a unique minimum and no maximum on \(I\).
The function \(f\) has a unique maximum and no minimum on \(I\).
The function \(f\) has a unique maximum and a unique minimum on \(I\).

2010016405

Level: 
B
In the following list identify a true statement about the function \(f(x) =\cos x\), where \(x\in \left[ -\frac{\pi }{2}; \frac{\pi } {2} \right] \).
The function \(f\) is neither increasing nor decreasing.
The function \(f\) is decreasing.
The function \(f\) is increasing.
The function \(f\) is increasing and decreasing.

2010016404

Level: 
C
Function \( f \) is given completely by the next graph. Identify which of the following statements is true.
\( f(x)=|-\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=|\sin x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\sin x|;\ x\in [ -2\pi;2\pi ]\)