What is the value of 3.25cos(pi/6*9)+19.15 ?

The value of 3.25cos(pi/6*9)+19.15 is (65cos((3pi)/2)+383)/(20)

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3.25cos(pi/6*9)+19.15

Solution

3.25 cos (\frac{π}{6} \cdot 9) + 19.15

Solution

\frac{65 cos ( \frac{3 π}{2} ) + 383}{20}

Decimal Notation

19.15

Solution steps

3.25 cos (\frac{π}{6} \cdot 9) + 19.15

= \frac{13}{4} cos (\frac{π}{6} \cdot 9) + \frac{383}{20}

Rewrite as

= cos (2 \cdot \frac{3 π}{4})

Rewrite using trig identities:

cos (2 \cdot \frac{3 π}{4}) = 1 - 2 sin^{2} (\frac{3 π}{4})

cos (2 \cdot \frac{3 π}{4})

Use the Double Angle identity:

cos (2 x) = 1 - 2 sin^{2} (x)

= 1 - 2 sin^{2} (\frac{3 π}{4})

= \frac{13}{4} cos (\frac{π}{6} \cdot 9) + \frac{383}{20}

Simplify:

\frac{π}{6} \cdot 9 = \frac{3 π}{2}

\frac{π}{6} \cdot 9

Multiply fractions:

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

= \frac{π 9}{6}

Cancel the common factor:

3

= \frac{3 π}{2}

\frac{13}{4} cos (\frac{3 π}{2}) + \frac{383}{20} = \frac{65 cos ( \frac{3 π}{2} ) + 383}{20}

\frac{13}{4} cos (\frac{3 π}{2}) + \frac{383}{20}

Multiply

\frac{13}{4} cos (\frac{3 π}{2}) : \frac{13 cos ( \frac{3 π}{2} )}{4}

\frac{13}{4} cos (\frac{3 π}{2})

Multiply fractions:

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

= \frac{13 cos ( \frac{3 π}{2} )}{4}

= \frac{13 cos ( \frac{3 π}{2} )}{4} + \frac{383}{20}

Least Common Multiplier of

4, 20 : 20

4, 20

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

Multiply each factor the greatest number of times it occurs in either

4

20

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

20

For

\frac{13 cos ( \frac{3 π}{2} )}{4} :

multiply the denominator and numerator by

5

\frac{13 cos ( \frac{3 π}{2} )}{4} = \frac{13 cos ( \frac{3 π}{2} ) \cdot 5}{4 \cdot 5} = \frac{65 cos ( \frac{3 π}{2} )}{20}

= \frac{65 cos ( \frac{3 π}{2} )}{20} + \frac{383}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{65 cos ( \frac{3 π}{2} ) + 383}{20}

= \frac{65 cos ( \frac{3 π}{2} ) + 383}{20}

Popular Examples

5/(sin(65))

\frac{5}{sin ( 6 5 ^{\circ} )}

arctan((-6)/5)

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3sin(300)

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sin(16.2)

sin (16. 2^{\circ})

-cos(2)+cos(1)

- cos (2) + cos (1)

Frequently Asked Questions (FAQ)

What is the value of 3.25cos(pi/6*9)+19.15 ?
The value of 3.25cos(pi/6*9)+19.15 is (65cos((3pi)/2)+383)/(20)