What is the value of -3+4cos(pi/3) ?

The value of -3+4cos(pi/3) is -1

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-3+4cos(pi/3)

- 3 + 4 cos (\frac{π}{3})

- 1

Solution steps

- 3 + 4 cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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}

= \frac{1}{2}

= - 3 + 4 \cdot \frac{1}{2}

Simplify

- 3 + 4 \cdot \frac{1}{2} : - 1

- 3 + 4 \cdot \frac{1}{2}

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

4 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 4}{2}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= - 3 + 2

Add/Subtract the numbers:

- 3 + 2 = - 1

= - 1

= - 1

tan (3 0^{\circ}) + cos (3 0^{\circ})

cos (\frac{π}{6}) - sin (\frac{π}{6})

sin (38 0^{\circ})

arccos (\frac{43}{48})

\frac{132}{tan ( 5 )}