What is the value of 5sin(pi/4)+5cos(pi/4) ?

The value of 5sin(pi/4)+5cos(pi/4) is 5sqrt(2)

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5sin(pi/4)+5cos(pi/4)

5 sin (\frac{π}{4}) + 5 cos (\frac{π}{4})

52

Decimal Notation

7.07106 \dots

Solution steps

5 sin (\frac{π}{4}) + 5 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}

= 5 \cdot \frac{2}{2} + 5 \cdot \frac{2}{2}

Simplify

5 \cdot \frac{2}{2} + 5 \cdot \frac{2}{2} : 52

5 \cdot \frac{2}{2} + 5 \cdot \frac{2}{2}

Add similar elements:

5 \cdot \frac{2}{2} + 5 \cdot \frac{2}{2} = 10 \cdot \frac{2}{2}

= 10 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 52

= 52

sin (17 π)

csc (arctan (\frac{1}{2}))

50 \cdot sin (3 7^{\circ})

sin (50.35 4^{\circ})

sec (\frac{- 4 π}{3})

What is the value of 5sin(pi/4)+5cos(pi/4) ?
The value of 5sin(pi/4)+5cos(pi/4) is 5sqrt(2)