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

The value of sin(pi/3)+cos(pi/3) is (sqrt(3)+1)/2

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

sin (\frac{π}{3}) + cos (\frac{π}{3})

\frac{3 + 1}{2}

Decimal Notation

1.36602 \dots

Solution steps

sin (\frac{π}{3}) + cos (\frac{π}{3})

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}{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}

= \frac{3}{2} + \frac{1}{2}

Simplify

\frac{3}{2} + \frac{1}{2} : \frac{3 + 1}{2}

\frac{3}{2} + \frac{1}{2}

Apply rule

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

= \frac{3 + 1}{2}

= \frac{3 + 1}{2}

arctan (\frac{3 3}{9})

6 sin (\frac{π}{2})

ln (2 + sin (\frac{7 π}{6}))

sin^{2} (4 5^{\circ}) + cos^{2} (3 0^{\circ})

arcsin (sin (2))

What is the value of sin(pi/3)+cos(pi/3) ?
The value of sin(pi/3)+cos(pi/3) is (sqrt(3)+1)/2