What is the value of 4cos^2(30)+6sin^2(30) ?

The value of 4cos^2(30)+6sin^2(30) is 9/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4cos^2(30)+6sin^2(30)

Solution

4 cos^{2} (3 0^{\circ}) + 6 sin^{2} (3 0^{\circ})

Solution

\frac{9}{2}

Decimal Notation

4.5

Solution steps

4 cos^{2} (3 0^{\circ}) + 6 sin^{2} (3 0^{\circ})

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}

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}

= 4 (\frac{3}{2})^{2} + 6 (\frac{1}{2})^{2}

Simplify

4 (\frac{3}{2})^{2} + 6 (\frac{1}{2})^{2} : \frac{9}{2}

4 (\frac{3}{2})^{2} + 6 (\frac{1}{2})^{2}

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

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

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

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

Apply exponent rule:

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

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

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

Multiply fractions:

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

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

Multiply the numbers:

3 \cdot 4 = 12

= \frac{12}{2 ^{2}}

Factor

12 : 2^{2} \cdot 3

Factor

12 = 2^{2} \cdot 3

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

Cancel the common factor:

2^{2}

= 3

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

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

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

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

Apply exponent rule:

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

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

Apply rule

1^{a} = 1

1^{2} = 1

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

= 6 \cdot \frac{1}{2 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 6}{2 ^{2}}

Multiply the numbers:

1 \cdot 6 = 6

= \frac{6}{2 ^{2}}

Factor

6 : 2 \cdot 3

Factor

6 = 2 \cdot 3

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

Cancel the common factor:

2

= \frac{3}{2}

= 3 + \frac{3}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 2 + 3 = 9

3 \cdot 2 + 3

Multiply the numbers:

3 \cdot 2 = 6

= 6 + 3

Add the numbers:

6 + 3 = 9

= 9

= \frac{9}{2}

= \frac{9}{2}

Popular Examples

ln(sec(pi/3)+tan(pi/3))

ln (sec (\frac{π}{3}) + tan (\frac{π}{3}))

cos(120)+tan^2(240)-5

cos (12 0^{\circ}) + tan^{2} (24 0^{\circ}) - 5

(cos(60))/(cos(45))

\frac{cos ( 6 0 ^{\circ} )}{cos ( 4 5 ^{\circ} )}

arctan(tan((5pi)/7))

arctan (tan (\frac{5 π}{7}))

sin^3(1)

sin^{3} (1)

Frequently Asked Questions (FAQ)

What is the value of 4cos^2(30)+6sin^2(30) ?
The value of 4cos^2(30)+6sin^2(30) is 9/2