Is cos(-pi/4)= 1/(sqrt(2)) ?

The answer to whether cos(-pi/4)= 1/(sqrt(2)) is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove cos(-pi/4)= 1/(sqrt(2))

prove

cos (- \frac{π}{4}) = \frac{1}{2}

True

Solution steps

cos (- \frac{π}{4}) = \frac{1}{2}

Manipulating left side

cos (- \frac{π}{4})

Use the negative angle identity:

cos (- x) = cos (x)

= cos (\frac{π}{4})

Expand

cos (\frac{π}{4}) : \frac{2}{2}

cos (\frac{π}{4})

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{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}

= \frac{2}{2}

= \frac{2}{2}

= \frac{1}{2}

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ( x ) + cot ( x )}{sec ( x ) csc ( x )} = 1

tan^{2} (a) + sin^{2} (a) = tan^{2} (a) sin^{2} (a)

tan (θ) sin (2 0^{\circ}) = 2 sin^{2} (θ)

\frac{1}{1 - sin ( x )} = - \frac{1}{sin ( x )}

tan (- a) = - tan (a)

Is cos(-pi/4)= 1/(sqrt(2)) ?
The answer to whether cos(-pi/4)= 1/(sqrt(2)) is True