What is the value of 5cos(5pi) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

5cos(5pi)

5 cos (5 π)

- 5

Solution steps

5 cos (5 π)

Rewrite using trig identities:

cos (5 π) = - 1

cos (5 π)

cos (5 π) = cos (π)

cos (5 π)

Rewrite

5 π

2 π \cdot 2 + π

= cos (2 π 2 + π)

Apply the periodicity of

cos

cos (x + 2 π \cdot k) = cos (x)

cos (2 π \cdot 2 + π) = cos (π)

= cos (π)

= cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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)

= - 1

= 5 (- 1)

Simplify

= - 5

arcsin (sin (3 0^{\circ}))

- 2 sec (0)

9 cos (0)

sin (8 0^{\circ}) cos (3 5^{\circ}) - cos (8 0^{\circ}) sin (3 5^{\circ})

arcsin (0.527)