1003076507
Level:
B
For which \( x \in[0;\frac{\pi}2] \) is \( \sin x = \cos x \)?
\( \frac{\pi}4 \)
\( 0 \)
\( \frac{\pi}2 \)
\( \frac{\pi}3 \)
Sine, cosine, tangent and cotangent
1003076508
Level:
B
For which \( \alpha\in[0;90^{\circ} ] \) is \( \mathrm{tg}\,\alpha = \mathrm{cotg}\,\alpha \)?
\( 45^{\circ} \)
\( 60^{\circ} \)
\( 35^{\circ} \)
\( 30^{\circ} \)
1003076509
Level:
B
At which point \( x\in(2\pi; 4\pi) \) has the function \( f(x)=\cos x \) a minimum?
\(3\pi\)
\(2 \pi \)
\( 4\pi \)
\( 3.5\pi \)
1003076510
Level:
B
If the angle \( \alpha\in[0;90^{\circ}] \) and \( \sin\alpha = 0.5 \), then \( \cos \alpha \) is equal to:
\( \frac{\sqrt3}2 \)
\( -\frac{\sqrt{3}}2 \)
\( -\frac12 \)
\( \frac12 \)
1003076511
Level:
B
If \( \mathrm{tg}\,x = 1 \), then \( \mathrm{cotg}\,x \) equals:
\( 1 \)
\( 0 \)
\( -1 \)
\( 0.5 \)
1003076512
Level:
B
The value of \( \sin\left(-\frac{53\pi}6\right) \) is the same as the value of
\( \sin\frac{7\pi}6 \).
\( \sin\frac{\pi}6 \).
\( \sin\frac{5\pi}6 \).
\( \sin\left( -\frac{11\pi}6 \right) \).
1003076513
Level:
B
If two of the values of \( \sin\alpha \), \( \cos\alpha \), \( \mathrm{tg}\alpha\) and \( \mathrm{cotg}\alpha \) are negative, then \( \alpha \) belongs to the interval
\( \left(\pi; \frac{3\pi}2 \right) \).
\( \left(0; \frac{\pi}2 \right) \).
\( \left(\frac{\pi}2; \pi\right) \).
\( \left( \frac{3\pi}2; 2\pi \right) \).
1003076514
Level:
B
By simplifying the expression \( \cos\left( \frac{\pi}2 - x \right) \) we get:
\( \sin x \)
\( \cos x \)
\( -\sin x \)
\( -\cos x \)
1003076515
Level:
B
By simplifying the expression \( \sin\left(\frac{\pi}2 - x \right) \) we get:
\( \cos x \)
\( \sin x \)
\( -\sin x \)
\( -\cos x \)
1003076601
Level:
B
How many \( x \)-intercepts has the graph of the function \( f(x)=\cos 2x \) on the interval \( [-\pi; 2\pi] \)?
\( 6 \)
\( 4 \)
\( 5 \)
\( 3 \)