Sine, cosine, tangent and cotangent

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.

2000005405

Level: 
B
Which of the following statements is true?
All values of the function \(f(x)=2-\cos x\) are positive.
Function \(f(x)=\mathrm{tg}\,x\) is increasing over the whole domain.
The smallest positive period of the function \(f(x)=\sin 4x\) is \(\frac{\pi}{4}\).
Function \(f(x)=1+\sin x\) is an odd function.