What is the value of -14.5cos(pi/8*60)+15.5 ?

The value of -14.5cos(pi/8*60)+15.5 is 31/2

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-14.5cos(pi/8*60)+15.5

Solution

- 14.5 cos (\frac{π}{8} \cdot 60) + 15.5

Solution

\frac{31}{2}

Decimal Notation

15.5

Solution steps

- 14.5 cos (\frac{π}{8} \cdot 60) + 15.5

= - \frac{29}{2} cos (\frac{π}{8} \cdot 60) + \frac{31}{2}

Simplify:

\frac{π}{8} \cdot 60 = \frac{15 π}{2}

\frac{π}{8} \cdot 60

Multiply fractions:

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

= \frac{π 60}{8}

Cancel the common factor:

4

= \frac{15 π}{2}

- \frac{29}{2} cos (\frac{15 π}{2}) + \frac{31}{2} = \frac{- 29 cos ( \frac{15 π}{2} ) + 31}{2}

- \frac{29}{2} cos (\frac{15 π}{2}) + \frac{31}{2}

Multiply

\frac{29}{2} cos (\frac{15 π}{2}) : \frac{29 cos ( \frac{15 π}{2} )}{2}

\frac{29}{2} cos (\frac{15 π}{2})

Multiply fractions:

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

= \frac{29 cos ( \frac{15 π}{2} )}{2}

= - \frac{29 cos ( \frac{15 π}{2} )}{2} + \frac{31}{2}

Apply rule

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

= \frac{- 29 cos ( \frac{15 π}{2} ) + 31}{2}

= \frac{- 29 cos ( \frac{15 π}{2} ) + 31}{2}

cos (\frac{15 π}{2}) = cos (\frac{3 π}{2})

cos (\frac{15 π}{2})

Rewrite

\frac{15 π}{2}

2 π \cdot 3 + \frac{3 π}{2}

= cos (2 π 3 + \frac{3 π}{2})

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 3 + \frac{3 π}{2}) = cos (\frac{3 π}{2})

= cos (\frac{3 π}{2})

= \frac{- 29 cos ( \frac{3 π}{2} ) + 31}{2}

Rewrite using trig identities:

cos (\frac{3 π}{2}) = 0

cos (\frac{3 π}{2})

Rewrite using trig identities:

cos (π) cos (\frac{π}{2}) - sin (π) sin (\frac{π}{2})

cos (\frac{3 π}{2})

Write

cos (\frac{3 π}{2})

cos (π + \frac{π}{2})

= cos (π + \frac{π}{2})

Use the Angle Sum identity:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (π) cos (\frac{π}{2}) - sin (π) sin (\frac{π}{2})

= cos (π) cos (\frac{π}{2}) - sin (π) sin (\frac{π}{2})

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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)

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

Use the following trivial identity:

sin (π) = 0

sin (π)

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= (- 1) \cdot 0 - 0 \cdot 1

Simplify

= 0

= \frac{- 29 \cdot 0 + 31}{2}

Simplify

= \frac{31}{2}

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Frequently Asked Questions (FAQ)

What is the value of -14.5cos(pi/8*60)+15.5 ?
The value of -14.5cos(pi/8*60)+15.5 is 31/2