B

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.

2000004702

Level: 
B
A part of a rectangle drawn on the wall is painted in yellow (see the picture). Imagine a bee landing on a random spot of the rectangle. What is the probability of the bee landing on the yellow part?
\( \frac{3}{8} \)
\( \frac{1}{3} \)
\( \frac{1}{8} \)
\( \frac{5}{8} \)