The arc is any part of a circle. It can be the part of section or segment. The arc length can be calculated by this formula below:

$$L=frac{pi R}{180}cdot theta$$ The arc of a circle.The sector of a circle is region bounded by two radius of equal length with a common center. The sector area can be calculated by this formula below:

$$A=frac{pi R^2}{360}cdot theta$$ The sector of a circle.The segment of a circle is a region bounded by a chord and one of the arcs connecting the chords endpoints. The area of a segment is the area of a sector minus the triangular. The segment area can be calculated by this formula below:

$$A=frac{pi R^2}{360}cdot theta-frac{R^2 sintheta}{2}$$ The segment of a circle. ]]>The **radius** is the distance between any point of the circle and the centre. The **diameter** is a line segment which goes straight across the circle and passes through the centre. The diameter is twice the radius: $D=2R$. The **circumference** is the distance around the circle. It can be calculated by these formulas below:

The **area** enclosed by a circle can be calculated by this formula below:

What is the circumference of a circle with radius of 3.5 cm? Round your answer to the nearest one.

$$C=2pi R=2cdot 3.14cdot 3.5 approx 22 text{ cm}$$What is the area of a circle with diameter of 5 cm? Round your answer to the nearest one.

$$A=pi R^2=3.14cdot left (frac{5}{2} right )^2 approx 20 text{ cm}^2$$What is the area of a circle with circumference of 30 cm? Round your answer to the nearest one.

$$C=2pi R, 30=2pi R, R=frac{15}{pi}$$ $$A=pi R^2=3.14cdot left (frac{15}{3.14} right )^2 approx 72 text{ cm}^2$$ ]]>The law of cosines works for any triangle. The only important thing is that side a faces angle A, side b faces angle B and side c faces angle C. It helps for correct using of formulas.

$$text{c}^2=text{a}^2+text{b}^2-2text{a}text{b}cos{text{C}}$$ Triangle. A, B, C are angles and a, b, c are sides.The formula above can be rewritten into these formulas, if we need to find other sides of triangle.

$$text{a}^2=text{b}^2+text{c}^2-2text{b}text{c}cos{text{A}}$$ $$text{b}^2=text{a}^2+text{c}^2-2text{a}text{c}cos{text{B}}$$It is not very necessary but for easier finding of triangle angles we can use these formulas below:

$$cos{text{C}}=frac{text{a}^2+text{b}^2-text{c}^2}{2text{a}text{b}}$$ $$cos{text{B}}=frac{text{a}^2+text{c}^2-text{b}^2}{2text{a}text{c}}$$ $$cos{text{A}}=frac{text{b}^2+text{c}^2-text{a}^2}{2text{b}text{c}}$$For triangle below find the side a. Round your answer to the nearest tenth.

$$text{a}^2=text{b}^2+text{c}^2-2text{b}text{c}cos{text{A}}$$ $$text{a}^2=text{17}^2+text{21}^2-2text{17}cdottext{21}cdotcos{text{55°}}$$ $$aapprox 17.9$$For triangle below find the angle A. Round your answer to the nearest one.

$$cos{text{A}}=frac{text{b}^2+text{c}^2-text{a}^2}{2text{b}text{c}}$$ $$cos{text{A}}=frac{text{29}^2+text{39}^2-text{35}^2}{2cdottext{29}cdottext{39}}=0.5026...$$ $$angle text{A}=cos^{-1}(0.5026...)approx 60°$$ ]]>The law of sines works for any triangle. The only important thing is that side a faces angle A, side b faces angle B and side c faces angle C. It helps for correct using of formulas.

$$frac{text{a}}{sintext{A}}=frac{text{b}}{sintext{B}}=frac{text{c}}{sintext{C}}$$ Triangle. A, B, C are angles and a, b, c are sides.For triangle below find the side a. Round your answer to the nearest tenth.

$$frac{text{a}}{sintext{45°}}=require{cancel} cancel{frac{text{b}}{sintext{B}}}=frac{text{40}}{sintext{35°}}$$ $$a=frac{text{40}}{sintext{35°}}cdot sintext{45°} approx 39.2$$For triangle below find the angle A. Round your answer to the nearest one.

$$frac{text{18}}{sintext{A}}=frac{text{23}}{sintext{75°}}=require{cancel} cancel{frac{text{c}}{sintext{C}}}$$ $$sintext{A}=frac{18cdot sintext{75°}}{23}= 0.7559...$$ $$angle text{A}=sin^{-1}(0.7559...)approx 49°$$ ]]>By using the following property we can rewrite radicals into exponential form and on the contrary.

$$a^{frac{m}{n}}=sqrt[n]{a^m}=(sqrt[n]{a})^m$$Rewrite radical $sqrt[5]{x^3}$ into exponential form.

$$sqrt[5]{x^3}=x^{frac{3}{5}}$$Simplify the expression $sqrt{x}cdot sqrt[3]{x}: sqrt[5]{x^2}$

$$sqrt{x}cdot sqrt[3]{x}: sqrt[5]{x^2}=x^{frac{1}{2}}cdot x^{frac{1}{3}}: x^{frac{2}{5}}=x^{frac{1}{2}+frac{1}{3}-frac{2}{5}}=x^{frac{13}{30}}=sqrt[30]{x^{13}}$$Simplify the expression $sqrt{xsqrt[3]{x^2}}$

$$sqrt{xsqrt[3]{x^2}}=x^{frac{1}{2}}cdot (x^{frac{2}{3}})^{frac{1}{2}}=x^{frac{1}{2}+frac{2}{3}cdot frac{1}{2}}=x^{frac{5}{6}}=sqrt[6]{x^{5}}$$ ]]>