What is the value of sin^2(30)cos^2(30) ?

The value of sin^2(30)cos^2(30) is 3/16

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(30)cos^2(30)

sin^{2} (3 0^{\circ}) cos^{2} (3 0^{\circ})

\frac{3}{16}

Decimal Notation

0.1875

Solution steps

sin^{2} (3 0^{\circ}) cos^{2} (3 0^{\circ})

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= (\frac{1}{2})^{2} (\frac{3}{2})^{2}

Simplify

(\frac{1}{2})^{2} (\frac{3}{2})^{2} : \frac{3}{16}

(\frac{1}{2})^{2} (\frac{3}{2})^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

(\frac{1}{2})^{2} (\frac{3}{2})^{2} = (\frac{1}{2} \cdot \frac{3}{2})^{2}

= (\frac{1}{2} \cdot \frac{3}{2})^{2}

\frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4}

\frac{1}{2} \cdot \frac{3}{2}

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 3}{2 \cdot 2}

Multiply:

1 \cdot 3 = 3

= \frac{3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3}{4}

= (\frac{3}{4})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 3 ) ^{2}}{4 ^{2}}

(3)^{2} : 3

Apply radical rule:

a = a^{\frac{1}{2}}

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= \frac{3}{4 ^{2}}

4^{2} = 16

= \frac{3}{16}

= \frac{3}{16}

sin^{2} (2 9^{\circ})

0.8 (70) (10) cos (3 7^{\circ})

sin (4 5^{\circ}) 8

90 tan (4 0^{\circ})

- sin (\frac{2}{2})

What is the value of sin^2(30)cos^2(30) ?
The value of sin^2(30)cos^2(30) is 3/16