What is the value of 8sin(pi/4)+8cos(pi/4) ?

The value of 8sin(pi/4)+8cos(pi/4) is 8sqrt(2)

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8sin(pi/4)+8cos(pi/4)

8 sin (\frac{π}{4}) + 8 cos (\frac{π}{4})

82

Decimal Notation

11.31370 \dots

Solution steps

8 sin (\frac{π}{4}) + 8 cos (\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}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

= 8 \cdot \frac{2}{2} + 8 \cdot \frac{2}{2}

Simplify

8 \cdot \frac{2}{2} + 8 \cdot \frac{2}{2} : 82

8 \cdot \frac{2}{2} + 8 \cdot \frac{2}{2}

Add similar elements:

8 \cdot \frac{2}{2} + 8 \cdot \frac{2}{2} = 16 \cdot \frac{2}{2}

= 16 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 16}{2}

Divide the numbers:

\frac{16}{2} = 8

= 82

= 82

sin (arccos (\frac{5}{7}))

\frac{10.8}{sin ( 5 7 ^{\circ} )}

tan (- 54 0^{\circ})

tan (0.6)

tan (2 arccos (\frac{3}{5}))

What is the value of 8sin(pi/4)+8cos(pi/4) ?
The value of 8sin(pi/4)+8cos(pi/4) is 8sqrt(2)