Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\cot \left(480°\right)=\cot \left(480-360°\right)$$

Subtracting one integer from another.

$$\cot \left(480-360°\right)=\cot \left(120°\right)$$

Reflecting the number with respect to 360 degrees.

$$\cot \left(120°\right)=\cot \left(180-60°\right)$$

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

$$\cot \left(180-60°\right)=\frac{\cos \left(180-60°\right)}{\sin \left(180-60°\right)}$$

Reflecting the cosine function with respect to 180 degrees.

$$\frac{\cos \left(180-60°\right)}{\sin \left(180-60°\right)}=\frac{-\cos \left(60°\right)}{\sin \left(180-60°\right)}$$

Reflecting the sine function with respect to 180 degrees.

$$\frac{-\cos \left(60°\right)}{\sin \left(180-60°\right)}=\frac{-\cos \left(60°\right)}{\sin \left(60°\right)}$$

Placing the minus sign in front of a fraction.

$$\frac{-\cos \left(60°\right)}{\sin \left(60°\right)}=-\frac{\cos \left(60°\right)}{\sin \left(60°\right)}$$

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

$$-\frac{\cos \left(60°\right)}{\sin \left(60°\right)}=-\cot \left(60°\right)$$

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

$$\cot \left(60°\right)=\frac{\cos \left(60°\right)}{\sin \left(60°\right)}$$

Computing the cosine of 60 degrees.

$$\frac{\cos \left(60°\right)}{\sin \left(60°\right)}=\frac{\frac{1}{2}}{\sin \left(60°\right)}$$

Computing the sine of 60 degrees.

$$\frac{\frac{1}{2}}{\sin \left(60°\right)}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}$$

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.

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