# Test: Trigonometric Equations I - Ambitious

Double click on maths expressions to zoom
Question 1:   Solve the equation $\text{\hspace{0.17em}}cos4x=-\frac{\sqrt{2}}{2}$ .
Question 2:   Solve the equation $\text{\hspace{0.17em}}\mathrm{sin}\left(t+\frac{\pi }{8}\right)=-1$ .
$-\frac{5\pi }{16}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$\frac{{\left(-1\right)}^{n+1}×5\pi }{8}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$-\frac{5\pi }{8}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$-\frac{5\pi }{8}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
Question 3:   Solve the equation .
$x=-\frac{\pi }{3}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=-\frac{\pi }{3}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=-\frac{\pi }{6}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=\frac{\pi }{3}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
Question 4:   Solve $\text{\hspace{0.17em}}arcsin\frac{3}{5}+arccos\frac{3}{5}$ .
$1$
$0$
$2\pi$
$\frac{\pi }{2}$
Question 5:   Solve the equation $\text{\hspace{0.17em}}arcctg\left(5-8x\right)=\frac{2\pi }{3}$ .
$\frac{15-2\pi }{24}$
$\frac{15+\sqrt{3}}{24}$
$\frac{5+\sqrt{3}}{8}$
$\frac{1}{2}$
Question 6:   Solve the inequality $\text{\hspace{0.17em}}1-cos2x-{\mathrm{sin}}^{2}x>0$ .
$x\in \left(0;1\right)$
Question 7:   Solve the equation $\text{\hspace{0.17em}}sin3x+sinx=sin2x$ .
Question 8:   Solve the inequality $\text{\hspace{0.17em}}ctgx\ge -\sqrt{3}$ .
$x\in \left(0;\frac{5\pi }{6}\right]$
Question 9:   Solve this system of equations $\text{\hspace{0.17em}}\left\{\begin{array}{c}x+y=\frac{\pi }{3}\\ sinx=1\end{array}\right\$ .
Question 10:   Solve the equation $\text{\hspace{0.17em}}tgx+\frac{1}{{\mathrm{cos}}^{2}x}=3$ .
$\frac{\pi }{4}+\pi n,\text{\hspace{0.17em}}n\in Ζ$