Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\tan \left(390°\right)=\tan \left(390-360°\right)$$

Subtracting one integer from another.

$$\tan \left(390-360°\right)=\tan \left(30°\right)$$

The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle.

$$\tan \left(30°\right)=\frac{\sin \left(30°\right)}{\cos \left(30°\right)}$$

Computing the sine of 30 degrees.

$$\frac{\sin \left(30°\right)}{\cos \left(30°\right)}=\frac{\frac{1}{2}}{\cos \left(30°\right)}$$

Computing the cosine of 30 degrees.

$$\frac{\frac{1}{2}}{\cos \left(30°\right)}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$$

Converting a fraction expression to multiplication by using the reciprocal of the denominator.

$$\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{2}\times \frac{2}{\sqrt{3}}$$

Multiplying two fractions together.

$$\frac{1}{2}\times \frac{2}{\sqrt{3}}=\frac{1\times 2}{2\times \sqrt{3}}$$

Multiplication can be done in any order, and the result remains the same.

$$\frac{1\times 2}{2\times \sqrt{3}}=\frac{1\times 2}{\sqrt{3}\times 2}$$

Distributing a fraction over multiplication.

$$\frac{1\times 2}{\sqrt{3}\times 2}=\frac{1}{\sqrt{3}}\times \frac{2}{2}$$

Distributing a fraction over multiplication.

$$\frac{1\times 2}{\sqrt{3}\times 2}=\frac{1}{\sqrt{3}}\times \frac{2}{2}$$

Dividing the same numbers.

$$\frac{1}{\sqrt{3}}\times \frac{2}{2}=\frac{1}{\sqrt{3}}\times 1$$

Distributing a fraction over multiplication.

$$\frac{1\times 2}{\sqrt{3}\times 2}=\frac{1}{\sqrt{3}}\times \frac{2}{2}$$

Dividing the same numbers.

$$\frac{1}{\sqrt{3}}\times \frac{2}{2}=\frac{1}{\sqrt{3}}\times 1$$

Multiplying a number by one, which does not change its value.

$$\frac{1}{\sqrt{3}}\times 1=\frac{1}{\sqrt{3}}$$

Multiplying the same number with the numerator and denominator of a fraction.

$$\frac{1}{\sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$$

Multiplying the same number with the numerator and denominator of a fraction.

$$\frac{1}{\sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$$

Multiplying the same numbers together.

$$\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3^2}}$$

Multiplying the same number with the numerator and denominator of a fraction.

$$\frac{1}{\sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$$

Multiplying the same numbers together.

$$\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3^2}}$$

Squaring the square root of a number.

$$\frac{1\times \sqrt{3}}{\sqrt{3^2}}=\frac{1\times \sqrt{3}}{3}$$

Multiplying the same number with the numerator and denominator of a fraction.

$$\frac{1}{\sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}$$

Multiplying the same numbers together.

$$\frac{1\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}=\frac{1\times \sqrt{3}}{\sqrt{3^2}}$$

Squaring the square root of a number.

$$\frac{1\times \sqrt{3}}{\sqrt{3^2}}=\frac{1\times \sqrt{3}}{3}$$

Multiplying a number by one, which does not change its value.

$$\frac{1\times \sqrt{3}}{3}=\frac{\sqrt{3}}{3}$$