What is the value of sin(pi/3)+cos(pi/6) ?

The value of sin(pi/3)+cos(pi/6) is square root of 3

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sin(pi/3)+cos(pi/6)

sin (\frac{π}{3}) + cos (\frac{π}{6})

3

Decimal Notation

1.73205 \dots

Solution steps

sin (\frac{π}{3}) + cos (\frac{π}{6})

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

sin (\frac{π}{3})

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}

= \frac{3}{2}

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

= \frac{3}{2} + \frac{3}{2}

Simplify

\frac{3}{2} + \frac{3}{2} : 3

\frac{3}{2} + \frac{3}{2}

Apply rule

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

= \frac{3 + 3}{2}

Add similar elements:

3 + 3 = 23

= \frac{2 3}{2}

Divide the numbers:

\frac{2}{2} = 1

= 3

= 3

cos (24 6^{\circ})

150 sin (4 5^{\circ})

sin (3 0^{\circ}) \cdot cos (6 0^{\circ})

arccos (- 0.93)

csc (7 7^{\circ})

What is the value of sin(pi/3)+cos(pi/6) ?
The value of sin(pi/3)+cos(pi/6) is square root of 3