What is the value of sin(3(pi/4)) ?

The value of sin(3(pi/4)) is (sqrt(2))/2

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sin(3(pi/4))

sin (3 (\frac{π}{4}))

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (3 (\frac{π}{4}))

= sin (3 \cdot \frac{π}{4})

Simplify:

3 \cdot \frac{π}{4} = \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 3}{4}

= sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 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}

cos (8 0^{\circ}) cos (1 0^{\circ}) - sin (8 0^{\circ}) sin (1 0^{\circ})

cot (5 4^{\circ})

arccot (- 8)

sin^{3} (\frac{3 π}{2})

cos (28. 5^{\circ})