Trigonometric Equations I - Ambitious

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Question 1: Solve the equation

c o s 4 x = - \frac{\sqrt{2}}{2}

\pm \frac{3 π}{4} + 2 π n, n \in Ζ

\pm \frac{{(- 1)}^{n + 1} \times π}{16} + \frac{π n}{4}, n \in Ζ

\pm \frac{3 π}{16} + \frac{π n}{2}, n \in Ζ

\pm \frac{3 π}{16} + 2 π n, n \in Ζ

Question 2: Solve the equation

\sin (t + \frac{π}{8}) = - 1

- \frac{5 π}{16} + 2 π n, n \in Ζ

\frac{{(- 1)}^{n + 1} \times 5 π}{8} + π n, n \in Ζ

- \frac{5 π}{8} + π n, n \in Ζ

- \frac{5 π}{8} + 2 π n, n \in Ζ

Question 3: Solve the equation

c t g x = - \frac{\sqrt{3}}{3}

x = - \frac{π}{6} + π n, n \in Ζ

x = - \frac{π}{3} + 2 π n, n \in Ζ

x = \frac{π}{3} + π n, n \in Ζ

x = - \frac{π}{3} + π n, n \in Ζ

Question 4: Solve

a r c s i n \frac{3}{5} + a r c c o s \frac{3}{5}

1

0

\frac{π}{2}

2 π

Question 5: Solve the equation

a r c c t g (5 - 8 x) = \frac{2 π}{3}

\frac{5 + \sqrt{3}}{8}

\frac{15 - 2 π}{24}

\frac{1}{2}

\frac{15 + \sqrt{3}}{24}

Question 6: Solve the inequality

1 - c o s 2 x - \sin^{2} x > 0

x \in (0; 1)

x \in (0; 2 π n), n \in Ζ

x \in (π n; π n + π), n \in Ζ

x \in (2 π n; 2 π n + π), n \in Ζ

Question 7: Solve the equation

s i n 3 x + s i n x = s i n 2 x

\frac{π n}{2}, \pm \frac{π}{3} + 2 π n, n \in Ζ

\pm \frac{π}{3} + 2 π n, n \in Ζ

\emptyset

x = \frac{π n}{2}, n \in Ζ

Question 8: Solve the inequality

c t g x \geq - \sqrt{3}

x \in (π n; \frac{5 π}{6} + π n], n \in Ζ

x \in (0; \frac{5 π}{6}]

x \in (π n; \frac{5 π}{6} + π n), n \in Ζ

x \in [π n; \frac{5 π}{6} + π n], n \in Ζ

Question 9: Solve this system of equations

\{\begin{matrix} x + y = \frac{π}{3} \\ s i n x = 1 \end{matrix}

(\frac{π}{2} - 2 π n; - \frac{π}{6} - 2 π n), n \in Ζ

(\frac{π}{2} + 2 π n; - \frac{π}{6} + 2 π n), n \in Ζ

(\frac{π}{2} + 2 π n; \frac{π}{6} - 2 π n), n \in Ζ

(\frac{π}{2} + 2 π n; - \frac{π}{6} - 2 π n), n \in Ζ

Question 10: Solve the equation

t g x + \frac{1}{\cos^{2} x} = 3

\frac{π}{4} + π n; - a r c t g 2 + π n, n \in Ζ

\frac{π}{4} + 2 π n; a r c t g 2 + 2 π n, n \in Ζ

\frac{π}{4}; - a r c t g 2

\frac{π}{4} + π n, n \in Ζ

Test: Trigonometric Equations I - Ambitious