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

The value of sin(pi/4)-sin(-pi/4) is square root of 2

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sin(pi/4)-sin(-pi/4)

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

2

Decimal Notation

1.41421 \dots

Solution steps

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

Use the following property:

sin (- x) = - sin (x)

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

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

Simplify

= 2 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}

= 2 \cdot \frac{2}{2}

Simplify

2 \cdot \frac{2}{2} : 2

2 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 2}{2}

Cancel the common factor:

2

= 2

= 2

arctan (e^{3})

csc (\frac{2 π}{9})

\frac{30}{tan ( 2 5 ^{\circ} )}

sin (- 49 5^{\circ})

cos (1 0^{\circ}) sin (9 2^{\circ})

What is the value of sin(pi/4)-sin(-pi/4) ?
The value of sin(pi/4)-sin(-pi/4) is square root of 2