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

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

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-cos(pi/2)-sin(pi/2)+cos(pi/4)+sin(pi/4)

- cos (\frac{π}{2}) - sin (\frac{π}{2}) + cos (\frac{π}{4}) + sin (\frac{π}{4})

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

- cos (\frac{π}{2}) - sin (\frac{π}{2}) + cos (\frac{π}{4}) + sin (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{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}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{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}

= - 0 - 1 + \frac{2}{2} + \frac{2}{2}

Simplify

- 0 - 1 + \frac{2}{2} + \frac{2}{2} : 2 - 1

- 0 - 1 + \frac{2}{2} + \frac{2}{2}

Combine the fractions

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

Divide the numbers:

\frac{2}{2} = 1

= 2

= - 0 - 1 + 2

Subtract the numbers:

- 0 - 1 = - 1

= 2 - 1

= 2 - 1

arcsin (\frac{35}{37})

arcsin (- \frac{2}{2})

tan (2 arcsin (- \frac{5}{13}))

cos (2 arcsin (\frac{7}{3}))

6 arctan (1)

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