What is the value of 9sin(pi/4)+9cos(pi/4) ?

The value of 9sin(pi/4)+9cos(pi/4) is 9sqrt(2)

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9sin(pi/4)+9cos(pi/4)

9 sin (\frac{π}{4}) + 9 cos (\frac{π}{4})

92

Decimal Notation

12.72792 \dots

Solution steps

9 sin (\frac{π}{4}) + 9 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}

= 9 \cdot \frac{2}{2} + 9 \cdot \frac{2}{2}

Simplify

9 \cdot \frac{2}{2} + 9 \cdot \frac{2}{2} : 92

9 \cdot \frac{2}{2} + 9 \cdot \frac{2}{2}

Add similar elements:

9 \cdot \frac{2}{2} + 9 \cdot \frac{2}{2} = 18 \cdot \frac{2}{2}

= 18 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 18}{2}

Divide the numbers:

\frac{18}{2} = 9

= 92

= 92

arccos (\frac{3}{14})

cos (2 (\frac{π}{4}))

arctan (\frac{5}{- 3})

sin (\frac{π}{2}) + cos (\frac{π}{2})

tan (\frac{9 π}{8})

What is the value of 9sin(pi/4)+9cos(pi/4) ?
The value of 9sin(pi/4)+9cos(pi/4) is 9sqrt(2)