# 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 $-90°$ .
$P1\left(-1;0\right)$
$P1\left(0;1\right)$
$P1\left(0;-1\right)$
$P1\left(0;0\right)$
Question 2:   Solve the expression $\text{\hspace{0.17em}}2{\text{sin}}^{2}\frac{\pi }{4}+{\text{cos}}^{2}\frac{\pi }{6}\text{\hspace{0.17em}}$ .
$1$
$1\frac{3}{4}$
$0$
$1.5$
Question 3:   Simplify the expression:  $\mathrm{sin}\alpha -\left|\mathrm{sin}\alpha \right|$,  if  $\alpha$  is located in the third coordinate quarter.
$1$
$2sin\alpha$
$sin\alpha$
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 $\text{\hspace{0.17em}}y=tg\frac{6x}{7}\text{\hspace{0.17em}}$ .
$\frac{7\pi }{6}$
$\frac{6\pi }{7}$
$\pi$
$2\pi$
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