Řešení - Trigonometry

Reflecting the number with respect to 360 degrees.

$$\cot \left(210°\right)=\cot \left(360-150°\right)$$

The period of trigonometric functions is 360 degrees.

$$\cot \left(360-150°\right)=\cot \left(360-150-360°\right)$$

Removing or simplifying the same numbers on the top and bottom of a fraction.

$$\cot \left(360-150-360°\right)=\cot \left(-150°\right)$$

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

$$\cot \left(-150°\right)=\frac{\cos \left(-150°\right)}{\sin \left(-150°\right)}$$

Computing the cosine of a negative angle.

$$\frac{\cos \left(-150°\right)}{\sin \left(-150°\right)}=\frac{\cos \left(150°\right)}{\sin \left(-150°\right)}$$

Computing the sine of a negative angle.

$$\frac{\cos \left(150°\right)}{\sin \left(-150°\right)}=\frac{\cos \left(150°\right)}{-\sin \left(150°\right)}$$

Placing the minus sign in front of a fraction.

$$\frac{\cos \left(150°\right)}{-\sin \left(150°\right)}=-\frac{\cos \left(150°\right)}{\sin \left(150°\right)}$$

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

$$-\frac{\cos \left(150°\right)}{\sin \left(150°\right)}=-\cot \left(150°\right)$$

Reflecting the number with respect to 360 degrees.

$$-\cot \left(150°\right)=-\cot \left(180-30°\right)$$

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

$$\cot \left(180-30°\right)=\frac{\cos \left(180-30°\right)}{\sin \left(180-30°\right)}$$

Reflecting the cosine function with respect to 180 degrees.

$$\frac{\cos \left(180-30°\right)}{\sin \left(180-30°\right)}=\frac{-\cos \left(30°\right)}{\sin \left(180-30°\right)}$$

Reflecting the sine function with respect to 180 degrees.

$$\frac{-\cos \left(30°\right)}{\sin \left(180-30°\right)}=\frac{-\cos \left(30°\right)}{\sin \left(30°\right)}$$

Placing the minus sign in front of a fraction.

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

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

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

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

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

Computing the cosine of 30 degrees.

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

Computing the sine of 30 degrees.

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

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

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

Multiplying two fractions together.

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

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

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

Distributing a fraction over multiplication.

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

Distributing a fraction over multiplication.

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

Dividing the same numbers.

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

Distributing a fraction over multiplication.

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

Dividing the same numbers.

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

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

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

The fraction equals its numerator if its denominator is one.

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