Trigonometric equations and inequalities

Solve the equation

$$\sin x=\frac{1}{2}.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$2\cos x-\sqrt{3}=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$\tan x=\sqrt{3}.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$3\sin x=4.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$\cos 3x=\cos x.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$\sin 2x=\sin \left(x+\frac{\pi }{4}\right).$$

Solution available to those who have unlocked the subject.

Solve the equation

$$\cos 2x=\sin x.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$2{\cos }^{2}x-7\cos x+3=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$3{\sin }^{2}x-4\sin x\cos x+{\cos }^{2}x=0.$$

Solution available to those who have unlocked the subject.

Solve the equation

$$\sin x-\cos x=1.$$

Solution available to those who have unlocked the subject.

Solve on $[0,2\pi )$ the inequality

$$\sin x\ge \frac{\sqrt{2}}{2}.$$

Solution available to those who have unlocked the subject.

Solve on $[0,2\pi )$ the inequality

$$2\cos x+1>0.$$

Solution available to those who have unlocked the subject.