# Test: Trigonometric Functions I - Challenging

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Question 1:   Find the coordinates of the point on the circle which was obtained by rotating of point $P\left(1;0\right)$ by the angle of $-90°$ .
$P1\left(0;-1\right)$
$P1\left(-1;0\right)$
$P1\left(0;1\right)$
$P1\left(0;0\right)$
Question 2:   Solve the expression $\text{\hspace{0.17em}}2{\text{sin}}^{2}\frac{\pi }{4}+{\text{cos}}^{2}\frac{\pi }{6}\text{\hspace{0.17em}}$ .
$0$
$1$
$1.5$
$1\frac{3}{4}$
Question 3:   Simplify the expression:  $\mathrm{sin}\alpha -\left|\mathrm{sin}\alpha \right|$,  if  $\alpha$  is located in the third coordinate quarter.
$2sin\alpha$
$sin\alpha$
$1$
Question 4:   Compare two expressions $\text{\hspace{0.17em}}\mathrm{sin}60°$ and $\text{\hspace{0.17em}}\mathrm{sin}\frac{7\pi }{6}\text{\hspace{0.17em}}$ .
Question 5:   Find the period ($\text{\hspace{0.17em}}T\text{\hspace{0.17em}}$ ) of the function $\text{\hspace{0.17em}}y=tg\frac{6x}{7}\text{\hspace{0.17em}}$ .
$\pi$
$\frac{6\pi }{7}$
$2\pi$
$\frac{7\pi }{6}$
Question 6:   Is the equation $\text{\hspace{0.17em}}cos\alpha =2cos59°\text{\hspace{0.17em}}$ possible?
No, it’s not
No, it’s not, unless $\text{\hspace{0.17em}}\alpha <0$
Yes, it is, only if $\text{\hspace{0.17em}}\alpha >0$
Yes, it is
Question 7:   Is the equation possible?
Yes, only if
No, unless
No, it’s not
Yes, it is
Question 8:   Find the answer of the expression $\text{\hspace{0.17em}}\frac{5cos\alpha +6sin\alpha }{2sin\alpha -5cos\alpha }\text{\hspace{0.17em}}$ , if $\text{\hspace{0.17em}}tg\alpha =\frac{1}{2}\text{\hspace{0.17em}}$ .
$-2cos\alpha$
Question 9:   Simplify the expression $\text{\hspace{0.17em}}tg10°+tg50°+\sqrt{3}tg10°tg50°\text{\hspace{0.17em}}$.
$\sqrt{3}$
$-\sqrt{3}$
$tg10°$
$tg50°$
Question 10:   Simplify the expression .
$-1$
$1$
$-ctgx$
$tgx$