Trigonometric equations I - Normal

Question 1: Solve the equation

\cos 2 x = - \frac{1}{2}

.

A

x = \pm \frac{π}{6} + π n

B

x = \pm \frac{π}{6} + 2 π n

C

x = \pm \frac{π}{3} + π n

D

x = \pm \frac{2 π}{3} + π n

Question 2: Solve the equations

\sin (x - \frac{π}{6}) = - \frac{\sqrt{2}}{2}

.

A

x = {(- 1)}^{n + 1} \times \frac{π}{4} + \frac{π}{6} + π n, n \in Z

B

x = {(- 1)}^{n + 1} \times \frac{π}{4} - \frac{π}{6} + 2 π n, n \in Z

C

x = {(- 1)}^{n + 1} \times \frac{π}{4} - \frac{π}{6} + π n, n \in Z

D

x = {(- 1)}^{n} \times \frac{π}{4} + \frac{π}{6} + π n, n \in Z

Question 3: Solve the equation

t g (- \frac{2 x}{3}) = - \sqrt{3}

.

A

x = \frac{π}{2} + \frac{3 π n}{2}, n \in Z

B

x = \frac{π}{4} + \frac{3 π n}{2}, n \in Z

C

x = \frac{π}{2} + π n, n \in Z

D

x = \frac{π}{3} + \frac{3 π n}{2}, n \in Z

Question 4: Solve the equation

c t g 6 x = 0

.

A

x = \frac{π}{12} + \frac{π n}{6}, n \in Z

B

x = \frac{π}{12} + \frac{π n}{12}, n \in Z

C

x = \frac{π}{6} + \frac{π n}{6}, n \in Z

D

x = \frac{π}{12} + π n, n \in Z

Question 5: Solve the expression

\sin (\arcsin \frac{π}{3})

.

A

\frac{\sqrt{3}}{2}

B

\frac{π}{6}

C

\frac{1}{2}

D

\frac{π}{3}

Question 6: Solve the expression

\cos (2 a r c t g (- \frac{1}{3}))

.

A

\frac{4}{5}

B

- \frac{4}{5}

C

\frac{2 \sqrt{3}}{3}

D

\frac{11}{9}

Question 7: Simplify the expression

\sin^{2} 4 α - \cos^{2} 4 α

.

A

- \cos 8 α

B

- \cos 4 α

C

1

D

\cos 8 α

Question 8: Simplify the expression

\cos^{2} 6 β + \sin^{2} (- 6 β)

.

A

-

\cos 2 β

B

\cos 2 β

C

- 1

D

1

Question 9: Solve the equation

\sin 2 x + \cos x = 0

.

A

x = \frac{π}{2} + π n, n \in Z

B

\emptyset

C

\begin{array}{l} x_{1} = \frac{π}{2} + π n, n \in Z \\ x_{2} = {(- 1)}^{n + 1} \times \frac{π}{6} + π n, n \in Z \end{array}

D

x = {(- 1)}^{n + 1} \times \frac{π}{6} + π n, n \in Z

Question 10: Solve the equation

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

.

A

\begin{array}{l} x_{1} = - 1 \\ x_{2} = 2 \end{array}

B

\emptyset

C

0

D

\begin{array}{l} x_{1} = 1 \\ x_{2} = - 2 \end{array}

Test: Trigonometric equations I - Normal

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