# Test: Trigonometric Equations I - Ambitious

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Question 1:   Solve the equation $\text{\hspace{0.17em}}cos4x=-\frac{\sqrt{2}}{2}$ .
Question 2:   Solve the equation $\text{\hspace{0.17em}}\mathrm{sin}\left(t+\frac{\pi }{8}\right)=-1$ .
$-\frac{5\pi }{16}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$-\frac{5\pi }{8}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$-\frac{5\pi }{8}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$\frac{{\left(-1\right)}^{n+1}×5\pi }{8}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
Question 3:   Solve the equation .
$x=-\frac{\pi }{3}+2\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=-\frac{\pi }{6}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=-\frac{\pi }{3}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
$x=\frac{\pi }{3}+\pi n,\text{\hspace{0.17em}}n\in Ζ$
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 $\text{\hspace{0.17em}}arcctg\left(5-8x\right)=\frac{2\pi }{3}$ .
$\frac{5+\sqrt{3}}{8}$
$\frac{15-2\pi }{24}$
$\frac{1}{2}$
$\frac{15+\sqrt{3}}{24}$
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