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

The value of sin(pi/4+pi/4) is 1

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sin(pi/4+pi/4)

sin (\frac{π}{4} + \frac{π}{4})

1

Solution steps

sin (\frac{π}{4} + \frac{π}{4})

Simplify:

\frac{π}{4} + \frac{π}{4} = \frac{π}{2}

\frac{π}{4} + \frac{π}{4}

Apply rule

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

= \frac{π + π}{4}

Add similar elements:

π + π = 2 π

= \frac{2 π}{4}

Cancel the common factor:

2

= \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

arccos (\frac{30}{40})

36 \cdot sin (6 0^{\circ})

tan^{2} (\frac{5}{3}) π + 4 sin (\frac{5}{6}) π - 3 cot^{2} (\frac{5}{4}) π

2 + 3 cos (π)

cos^{2} (\frac{90}{2})