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

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

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

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

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

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

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{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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{2}{2}

= - \frac{2}{2} - \frac{2}{2}

Simplify

- \frac{2}{2} - \frac{2}{2} : - 2

- \frac{2}{2} - \frac{2}{2}

Apply rule

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

= \frac{- 2 - 2}{2}

Add similar elements:

- 2 - 2 = - 22

= \frac{- 2 2}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{2 2}{2}

Divide the numbers:

\frac{2}{2} = 1

= - 2

= - 2

\frac{2 \cdot ( cos ( 4 5 ^{\circ} ) ) ^{2} + 3 \cdot csc ( 3 7 ^{\circ} )}{2 tan ( 4 5 ^{\circ} )}

sin (arcsin (\frac{3}{5}) + arccos (- \frac{5}{13}))

arccos (\frac{- 2}{14})

arccos (\frac{3}{2}) + arccos (\frac{1}{2})

arccsc (csc (\frac{4 π}{3}))

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