What is the value of -cos(pi/4)-(-cos(0)) ?

The value of -cos(pi/4)-(-cos(0)) is -(sqrt(2))/2+1

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-cos(pi/4)-(-cos(0))

- cos (\frac{π}{4}) - (- cos (0))

- \frac{2}{2} + 1

Decimal Notation

0.29289 \dots

Solution steps

- cos (\frac{π}{4}) - (- cos (0))

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:

cos (0) = 1

cos (0)

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}

= 1

= - \frac{2}{2} - (- 1)

Simplify

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

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

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

\frac{15}{tan ( 3 0 ^{\circ} )}

sin (2) (50)

arcsin (sec (0))

What is the value of -cos(pi/4)-(-cos(0)) ?
The value of -cos(pi/4)-(-cos(0)) is -(sqrt(2))/2+1