Trigonometric Equations I - Challenging

Question 1: Solve the equation

\cos (\frac{π}{8} - 4 x) = 1

.

A

x = \frac{π}{32} - \frac{π n}{2}, n \in Ζ

B

x = \frac{π}{32} - 2 π n, n \in Ζ

C

x = \frac{π}{8} - 2 π n, n \in Ζ

D

x = \frac{π}{8} - \frac{π n}{2}, n \in Ζ

Question 2: Find the biggest negative root of the equation

\sin (3 x - \frac{π}{15}) = - 1

.

A

x = - \frac{13 π}{45}

B

x = - \frac{17 π}{90}

C

x = - \frac{13 π}{90}

D

x = - π

Question 3: Find the sum of the roots of the equation

t g 2 x = - \sqrt{3}

, which belong to the range

[- π; \frac{π}{2}]

.

A

\frac{π}{6}

B

- \frac{π}{3}

C

- \frac{π}{2}

D

- \frac{5 π}{6}

Question 4: Solve the equation

a r c c o s x = \frac{1}{3}

.

A

s i n \frac{1}{3}

B

c o s \frac{1}{3}

C

\frac{1}{3}

D

\frac{π}{3}

Question 5: Solve the inequality

a r c t g (4 x - 5) > - \frac{π}{3}

.

A

x \in (- \infty; \frac{5 - \sqrt{3}}{4})

B

x \in (\frac{5 - \sqrt{3}}{4}; + \infty)

C

x \in (- 5; \frac{π}{3})

D

x \in (- \frac{π}{3}; 5)

Test: Trigonometric Equations I - Challenging