What is the value of 2sin(pi)-cos^7(pi)+sqrt(pi) ?

The value of 2sin(pi)-cos^7(pi)+sqrt(pi) is sqrt(pi)+1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2sin(pi)-cos^7(pi)+sqrt(pi)

2 sin (π) - cos^{7} (π) + π

π + 1

Decimal Notation

2.77245 \dots

Solution steps

2 sin (π) - cos^{7} (π) + π

Use the following trivial identity:

sin (π) = 0

sin (π)

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}

= 0

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)

= 2 \cdot 0 - (- 1)^{7} + π

Simplify

2 \cdot 0 - (- 1)^{7} + π : π + 1

2 \cdot 0 - (- 1)^{7} + π

2 \cdot 0 = 0

2 \cdot 0

Apply rule

0 \cdot a = 0

= 0

(- 1)^{7} = - 1

(- 1)^{7}

Apply exponent rule:

(- a)^{n} = - a^{n},

n

is odd

(- 1)^{7} = - 1^{7}

= - 1^{7}

Apply rule

1^{a} = 1

= - 1

= 0 - (- 1) + π

Apply rule

- (- a) = a

= 0 + 1 + π

Add the numbers:

0 + 1 = 1

= π + 1

= π + 1

tan^{2} (5 0^{\circ})

cos (1) - cos (2)

\frac{1}{sin ( 1 5 ^{\circ} )}

8 cos (4)

cos (\frac{π}{3}) cos (\frac{π}{6}) + sin (\frac{π}{3}) sin (\frac{π}{6})

What is the value of 2sin(pi)-cos^7(pi)+sqrt(pi) ?
The value of 2sin(pi)-cos^7(pi)+sqrt(pi) is sqrt(pi)+1