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

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

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

- 2 sin (- \frac{π}{2}) - 1

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

- 2 sin (- \frac{π}{2}) - 1

Rewrite using trig identities:

sin (- \frac{π}{2}) = - 1

sin (- \frac{π}{2})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{2}) = - sin (\frac{π}{2})

= - sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= - 1

= - 2 (- 1) - 1

Simplify

= 2 - 1

sin (233.1 3^{\circ})

sin (123 0^{\circ})

2 sin (\frac{1}{2}) π

\frac{sin ( 2 0 ^{\circ} ) \cdot 350}{sin ( 5 0 ^{\circ} )}

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

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