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

The value of sin(-(3pi)/4)+cos(-pi/3) is (-sqrt(2)+1)/2

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sin(-(3pi)/4)+cos(-pi/3)

sin (- \frac{3 π}{4}) + cos (- \frac{π}{3})

\frac{- 2 + 1}{2}

Decimal Notation

- 0.20710 \dots

Solution steps

sin (- \frac{3 π}{4}) + cos (- \frac{π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{3}) = cos (\frac{π}{3})

= sin (- \frac{3 π}{4}) + cos (\frac{π}{3})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{3 π}{4}) = - sin (\frac{3 π}{4})

= - sin (\frac{3 π}{4}) + cos (\frac{π}{3})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

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

Simplify

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

- \frac{2}{2} + \frac{1}{2}

Apply rule

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

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

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

arctan (\frac{6}{1}) + 180

sin (\frac{π}{2} \cdot 4)

arccos (\frac{13}{24})

sin (2 (\frac{π}{8}))

arcsin (\frac{( 7 sin ( 14 5 ^{\circ} ) )}{37})

What is the value of sin(-(3pi)/4)+cos(-pi/3) ?
The value of sin(-(3pi)/4)+cos(-pi/3) is (-sqrt(2)+1)/2