Sine, Cosine, Tangent, and Cotangent

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.
\( f(x)=|-\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\cos x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=|\sin x|;\ x\in [ -2\pi;2\pi ]\)
\( f(x)=-|\sin x|;\ x\in [ -2\pi;2\pi ]\)

2000005406

Level: 
B
Which of the following statements is not true?
Functions \(f(x)=\cos\left(x+\frac{\pi}{6}\right)\) and \(g(x)=\sin\left(x-\frac{\pi}{6}\right)\) are equal.
Functions \(f(x)=2-\cos 3x\) is even and its range of values is \([ 1;3]\).
Functions \(f(x)=\cos\left(x-\frac{\pi}{3}\right)\) and \(g(x)=\sin\left(x+\frac{\pi}{6}\right)\) are equal.
Functions \(f(x)=\cos x\) and \(g(x)=\sin\left(x+\frac{\pi}{2}\right)\) are equal.