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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

-sqrt(2)sin(-pi/4)-1

- 2 sin (- \frac{π}{4}) - 1

0

Solution steps

- 2 sin (- \frac{π}{4}) - 1

Rewrite using trig identities:

sin (- \frac{π}{4}) = - \frac{2}{2}

sin (- \frac{π}{4})

Use the following property:

sin (- x) = - sin (x)

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

= - sin (\frac{π}{4})

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}

= - \frac{2}{2}

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

Simplify

- 2 (- \frac{2}{2}) - 1 : 0

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

Apply rule

- (- a) = a

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

2 \frac{2}{2} = 1

2 \frac{2}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 2}{2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1 - 1

Subtract the numbers:

1 - 1 = 0

= 0

= 0

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