# Test: Trigonometric Functions I - Ambitious

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Question 1:   Compare these two angles expressed in radians: $\text{\hspace{0.17em}}\frac{\pi }{4}\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}1$ .
$\frac{\pi }{4}<1$
$\frac{\pi }{4}=1$
$\frac{\pi }{4}>1$
$\frac{\pi }{4}\ge 1$
Question 2:   Solve the expression $\text{\hspace{0.17em}}sin0+tg\pi -cos2\pi$ .
$-\frac{1}{2}$
$0$
$-1$
$1$
Question 3:   Which of these functions can be equal to $\text{\hspace{0.17em}}\frac{\sqrt{6}}{2}\text{\hspace{0.17em}}$ :

1) and 3)
1) and 2)
2)
3)
Question 4:   Solve the expression $\text{\hspace{0.17em}}{\mathrm{sin}}^{2}\left(-30°\right)+{\mathrm{cos}}^{2}\left(-60°\right)$ .
$\frac{1+\sqrt{3}}{2}$
$\frac{\sqrt{3}-1}{2}$
$-\frac{1}{2}$
$\frac{1}{2}$
Question 5:   Compare two expressions: $\text{\hspace{0.17em}}sin20°\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}sin21°$ .
$sin20°>sin21°$
$sin20°\le sin21°$
$sin20°=sin21°$
$sin20°
Question 6:   Compare two expressions: and .
Question 7:   Simplify the expression $\text{\hspace{0.17em}}{\left(1+ctg\beta \right)}^{2}+{\left(1-ctg\beta \right)}^{2}$ .
$2$
$2ctg\beta$
$\frac{2}{{\mathrm{sin}}^{2}\beta }$
$\frac{1}{{\mathrm{sin}}^{2}\beta }$
Question 8:   Simplify the expression $\text{\hspace{0.17em}}\mathrm{sin}\left(30°-\alpha \right)+\text{cos}\left(60°-\alpha \right)$ .
$\frac{sin\alpha }{2}$
$\sqrt{3}sin\alpha$
$cos\alpha$
$\frac{cos\alpha -\sqrt{3}sin\alpha }{2}$
Question 9:   Simplify the expression  $tg\left(\frac{\pi }{2}+\alpha \right)-ctg\left(\pi -\alpha \right)$ .
$tg\alpha$
$1$
$0$
$-ctg\frac{\alpha }{2}$
Question 10:   Simplify the expression $\text{\hspace{0.17em}}\frac{1-cos2\alpha }{{\mathrm{sin}}^{2}\alpha }$ .
$2$
$1$
$ctg\alpha$
$-tg\alpha$