Řešení - Trigonometry

The period of trigonometric functions is 360 degrees.

$$\csc \left(405°\right)=\csc \left(405-360°\right)$$

Subtracting one integer from another.

$$\csc \left(405-360°\right)=\csc \left(45°\right)$$

The cosecant of an angle is equal to one divided by the sine of the angle.

$$\csc \left(45°\right)=\frac{1}{\sin \left(45°\right)}$$

Computing the sine of 45 degrees.

$$\frac{1}{\sin \left(45°\right)}=\frac{1}{\frac{\sqrt{2}}{2}}$$

Computing the reciprocal of a fraction.

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

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

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

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

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

Multiplying the same numbers together.

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

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

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

Multiplying the same numbers together.

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

Squaring the square root of a number.

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

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

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