What is the value of 1/2 12^2sin(90) ?

The value of 1/2 12^2sin(90) is 72

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1/2 12^2sin(90)

\frac{1}{2} 1 2^{2} sin (9 0^{\circ})

72

Solution steps

\frac{1}{2} \cdot 1 2^{2} sin (9 0^{\circ})

Use the following trivial identity:

sin (9 0^{\circ}) = 1

sin (9 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}

= 1

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

Simplify

\frac{1}{2} \cdot 1 2^{2} \cdot 1 : 72

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

Multiply fractions:

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

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

\frac{1 \cdot 1 2 ^{2}}{2} = 72

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

Multiply:

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

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

Factor

1 2^{2} : 2^{4} \cdot 3^{2}

Factor

12 = 2^{2} \cdot 3

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

Apply exponent rule:

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

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

Simplify

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

Apply exponent rule:

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

= 2^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 2^{4}

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

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

Cancel the common factor:

2

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

2^{3} = 8

= 3^{2} \cdot 8

3^{2} = 9

= 8 \cdot 9

Multiply the numbers:

8 \cdot 9 = 72

= 72

= 1 \cdot 72

Multiply the numbers:

1 \cdot 72 = 72

= 72

= 72

2 + 2 cos (2 π)

arctan (\frac{6}{3})

\frac{6}{cos ( 3 3 ^{\circ} )}

337 cos (149 0^{\circ}) + 1490

arccos (\frac{15}{21})