# Test: Trigonometric functions I - Normal

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Question 1:   Convert $\text{\hspace{0.17em}}25°\text{\hspace{0.17em}}$ to radians.
$\frac{7\pi }{36}$
$\frac{2\pi }{3}$
$\frac{5\pi }{36}$
$\frac{\pi }{2}$
Question 2:   Convert $\text{\hspace{0.17em}}\frac{11\pi }{6}\text{\hspace{0.17em}}$ to degrees.
$270°$
$45°$
$225°$
$330°$
Question 3:   A radian measure of an $\text{\hspace{0.17em}}arc\left(\alpha \right)\text{\hspace{0.17em}}$ in a circle equals $\text{\hspace{0.17em}}\frac{3\pi }{4}\text{\hspace{0.17em}}$ while radius $\text{\hspace{0.17em}}\left(R\right)\text{\hspace{0.17em}}$ equals  $5cm$ .  What is the length $\text{\hspace{0.17em}}\left(l\right)\text{\hspace{0.17em}}$ of this arc?
$\text{\hspace{0.17em}}\frac{15\pi }{4}\text{\hspace{0.17em}}$
$\text{\hspace{0.17em}}\frac{3\pi }{20}\text{\hspace{0.17em}}$
$\text{\hspace{0.17em}}\frac{20\pi }{3}\text{\hspace{0.17em}}$
$\text{\hspace{0.17em}}\frac{4\pi }{15}\text{\hspace{0.17em}}$
Question 4:   Solve the expression $\text{\hspace{0.17em}}3tg180°-4ctg90°\text{\hspace{0.17em}}$.
$-1$
$3$
$0$
$-7$
Question 5:   Solve the expression $\text{\hspace{0.17em}}\mathrm{cos}\left(-60°\right)+ctg\left(-45°\right)\text{\hspace{0.17em}}$ .
$-1$
$-\frac{1}{2}$
$1$
$0$
Question 6:   Solve $\text{\hspace{0.17em}}\mathrm{sin}660°\text{\hspace{0.17em}}$ .
$\frac{\sqrt{3}}{2}$
$\frac{1}{2}$
$-\frac{\sqrt{3}}{2}$
$-\frac{1}{2}$
Question 7:   Which interval is decreasing for function $\text{\hspace{0.17em}}y=\mathrm{cos}x\text{\hspace{0.17em}}$ .
Question 8:   Which of this points the graph of function $\text{\hspace{0.17em}}y=tgx\text{\hspace{0.17em}}$ crosses?
$\left[-\frac{\pi }{2};0\right]$
$\left[\frac{\pi }{2};0\right]$
$\left[-\frac{\pi }{4};1\right]$
$\left[\frac{\pi }{4};1\right]$
Question 9:   Simplify the expression $\text{\hspace{0.17em}}1-{\mathrm{sin}}^{2}\alpha +ct{g}^{2}\alpha ×{\mathrm{sin}}^{2}\alpha \text{\hspace{0.17em}}$ .
$1-{\mathrm{cos}}^{2}\alpha$
$-1$
$1$
$0$
Question 10:   Simplify the expression $\text{\hspace{0.17em}}\mathrm{cos}\left(\alpha +\beta \right)+\mathrm{cos}\left(\alpha -\beta \right)\text{\hspace{0.17em}}$ .
$2\mathrm{sin}\alpha \mathrm{sin}\beta$
$\mathrm{cos}\alpha \mathrm{cos}\beta$
$\mathrm{sin}\alpha \mathrm{sin}\beta$
$2\mathrm{cos}\alpha \mathrm{cos}\beta$