What is the value of 7sin(pi/4)+7cos(pi/4) ?

The value of 7sin(pi/4)+7cos(pi/4) is 7sqrt(2)

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7sin(pi/4)+7cos(pi/4)

7 sin (\frac{π}{4}) + 7 cos (\frac{π}{4})

72

Decimal Notation

9.89949 \dots

Solution steps

7 sin (\frac{π}{4}) + 7 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}

= 7 \cdot \frac{2}{2} + 7 \cdot \frac{2}{2}

Simplify

7 \cdot \frac{2}{2} + 7 \cdot \frac{2}{2} : 72

7 \cdot \frac{2}{2} + 7 \cdot \frac{2}{2}

Add similar elements:

7 \cdot \frac{2}{2} + 7 \cdot \frac{2}{2} = 14 \cdot \frac{2}{2}

= 14 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 14}{2}

Divide the numbers:

\frac{14}{2} = 7

= 72

= 72

6 \cdot cos (3 0^{\circ})

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

\frac{4.3}{tan ( 3 0 ^{\circ} )}

\frac{4}{tan ( 3 0 ^{\circ} )}

\frac{100}{tan ( 2 5 ^{\circ} )}

What is the value of 7sin(pi/4)+7cos(pi/4) ?
The value of 7sin(pi/4)+7cos(pi/4) is 7sqrt(2)