What is the value of (sin(60)+1)^2 ?

The value of (sin(60)+1)^2 is sqrt(3)+7/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(sin(60)+1)^2

(sin (6 0^{\circ}) + 1)^{2}

3 + \frac{7}{4}

Decimal Notation

3.48205 \dots

Solution steps

(sin (6 0^{\circ}) + 1)^{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

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

Simplify

(\frac{3}{2} + 1)^{2} : 3 + \frac{7}{4}

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

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = \frac{3}{2}, b = 1

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

Simplify

(\frac{3}{2})^{2} + 2 \cdot \frac{3}{2} \cdot 1 + 1^{2} : 3 + \frac{7}{4}

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

Apply rule

1^{a} = 1

1^{2} = 1

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

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

(\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}}

2^{2} = 4

= \frac{3}{4}

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

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 1 \cdot 3

Multiply:

1 \cdot 3 = 3

= 3

= \frac{3}{4} + 3 + 1

Combine the fractions

1 + \frac{3}{4} : \frac{7}{4}

1 + \frac{3}{4}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

1 \cdot 4 + 3 = 7

1 \cdot 4 + 3

Multiply the numbers:

1 \cdot 4 = 4

= 4 + 3

Add the numbers:

4 + 3 = 7

= 7

= \frac{7}{4}

= 3 + \frac{7}{4}

= 3 + \frac{7}{4}

= 3 + \frac{7}{4}

59 - 25 cos^{2} (0) - 50 sin (0)

arctan (\frac{2.2907}{1.6326})

sin (- 1 \frac{1}{2})

cos (6 0^{\circ}) 6

cos^{2} (1 0^{\circ}) - sin^{2} (1 0^{\circ})