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

The value of 2(30)cos^2(30) is pi/4

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2(30)cos^2(30)

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

\frac{π}{4}

Decimal Notation

0.78539 \dots

Solution steps

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

= 2 \cdot 3 0^{\circ} cos^{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}

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

Simplify

2 \cdot 3 0^{\circ} (\frac{3}{2})^{2} : 4 5^{\circ}

2 \cdot 3 0^{\circ} (\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}}

= 2 \cdot 3 0^{\circ} \cdot \frac{3}{2 ^{2}}

Multiply fractions:

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

= \frac{18 0 ^{\circ} 3 \cdot 2}{6 \cdot 2 ^{2}}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{108 0 ^{\circ}}{2 ^{2} \cdot 6}

Divide the numbers:

\frac{6}{6} = 1

= \frac{18 0 ^{\circ}}{2 ^{2}}

2^{2} = 4

= 4 5^{\circ}

= 4 5^{\circ}

2 - 2 sin (2)

tan (- 60 0^{\circ})

\frac{1}{4} sin (4 π)

e^{π - π} tan (29 π)

129.5 sin (3 2^{\circ})