What is the value of ((325*cos(2pi*50))^2)/(10) ?

The value of ((325*cos(2pi*50))^2)/(10) is 21125/2

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((325cos(2pi50))^2)/(10)

\frac{( 325 \cdot cos ( 2 π \cdot 50 ) ) ^{2}}{10}

\frac{21125}{2}

Decimal Notation

10562.5

Solution steps

\frac{( 325 cos ( 2 π 50 ) ) ^{2}}{10}

Simplify:

2 π 50 = 100 π

2 π 50

Multiply the numbers:

2 \cdot 50 = 100

= 100 π

\frac{( 325 cos ( 100 π ) ) ^{2}}{10} = \frac{21125 cos ^{2} ( 100 π )}{2}

\frac{( 325 cos ( 100 π ) ) ^{2}}{10}

Factor

(325 cos (100 π))^{2} : 5^{4} \cdot 1 3^{2} cos^{2} (100 π)

Factor

325 = 5^{2} \cdot 13

= (5^{2} \cdot 13 cos (100 π))^{2}

Apply exponent rule:

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

= 1 3^{2} cos^{2} (100 π) (5^{2})^{2}

Simplify

(5^{2})^{2} : 5^{4}

(5^{2})^{2}

Apply exponent rule:

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

= 5^{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= 5^{4}

= 5^{4} \cdot 1 3^{2} cos^{2} (100 π)

Factor

10 : 2 \cdot 5

Factor

10 = 2 \cdot 5

= \frac{5 ^{4} \cdot 1 3 ^{2} cos ^{2} ( 100 π )}{2 \cdot 5}

Cancel the common factor:

5

= \frac{5 ^{3} \cdot 1 3 ^{2} cos ^{2} ( 100 π )}{2}

5^{3} \cdot 1 3^{2} cos^{2} (100 π) = 21125 cos^{2} (100 π)

5^{3} \cdot 1 3^{2} cos^{2} (100 π)

5^{3} = 125

= 1 3^{2} \cdot 125 cos^{2} (100 π)

1 3^{2} = 169

= 125 \cdot 169 cos^{2} (100 π)

Multiply the numbers:

125 \cdot 169 = 21125

= 21125 cos^{2} (100 π)

= \frac{21125 cos ^{2} ( 100 π )}{2}

= \frac{21125 cos ^{2} ( 100 π )}{2}

cos (100 π) = cos (0)

cos (100 π)

Rewrite

100 π

2 π \cdot 50 + 0

= cos (2 π 50 + 0)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 50 + 0) = cos (0)

= cos (0)

= \frac{21125 cos ^{2} ( 0 )}{2}

Use the following trivial identity:

cos (0) = 1

cos (0)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{21125 \cdot 1 ^{2}}{2}

Simplify

= \frac{21125}{2}

sin^{2} (- 9 0^{\circ})

400 cos (2 5^{\circ}) + 700 cos (8 0^{\circ})

arctan (\frac{40}{70})

arcsec (1.632)

sin (27 5^{\circ})

What is the value of ((325*cos(2pi*50))^2)/(10) ?
The value of ((325*cos(2pi*50))^2)/(10) is 21125/2