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Popular Trigonometry >

5+4cos(pi/3)

Solution

5 + 4 cos (\frac{π}{3})

Solution

7

Solution steps

5 + 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}

= 5 + 4 \cdot \frac{1}{2}

Simplify

5 + 4 \cdot \frac{1}{2} : 7

5 + 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

= 5 + 2

Add the numbers:

5 + 2 = 7

= 7

= 7

Popular Examples

(cos(pi/6))/((1-sin(pi/6))^2)

3arctan(1/7)+2arctan(2/11)

ln(sec(pi/2)+tan(pi/2))

Frequently Asked Questions (FAQ)

What is the value of 5+4cos(pi/3) ?
The value of 5+4cos(pi/3) is 7