What is the value of 371*cos(90-45)+695.1cos(45) ?

The value of 371*cos(90-45)+695.1cos(45) is (10661sqrt(2))/(20)

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371*cos(90-45)+695.1cos(45)

371 \cdot cos (9 0^{\circ} - 4 5^{\circ}) + 695.1 cos (4 5^{\circ})

\frac{10661 2}{20}

Decimal Notation

753.84653 \dots

Solution steps

371 cos (9 0^{\circ} - 4 5^{\circ}) + 695.1 cos (4 5^{\circ})

= 371 cos (9 0^{\circ} - 4 5^{\circ}) + \frac{6951}{10} cos (4 5^{\circ})

Simplify

= \frac{10661 cos ( 4 5 ^{\circ} )}{10}

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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}

= \frac{10661 \cdot \frac{2}{2}}{10}

Simplify

\frac{10661 \cdot \frac{2}{2}}{10} : \frac{10661 2}{20}

\frac{10661 \cdot \frac{2}{2}}{10}

Multiply

10661 \cdot \frac{2}{2} : \frac{10661}{2}

10661 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 10661}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{10661 \cdot 2 ^{\frac{1}{2}}}{2}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{10661}{2 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{10661}{2 ^{\frac{1}{2}}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{10661}{2}

= \frac{\frac{10661}{2}}{10}

Apply the fraction rule:

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

= \frac{10661}{2 \cdot 10}

Rationalize

\frac{10661}{10 2} : \frac{10661 2}{20}

\frac{10661}{10 2}

Multiply by the conjugate

\frac{2}{2}

= \frac{10661 2}{2 \cdot 10 2}

2 \cdot 102 = 20

2 \cdot 102

Apply radical rule:

a a = a

22 = 2

= 10 \cdot 2

Multiply the numbers:

10 \cdot 2 = 20

= 20

= \frac{10661 2}{20}

= \frac{10661 2}{20}

= \frac{10661 2}{20}

sin (5) π^{\circ}

600 cosh (\frac{0}{600})

- 2 sinh (1 - 2)

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

arctan (\frac{2.77}{9.8} + 0.6)

What is the value of 371*cos(90-45)+695.1cos(45) ?
The value of 371*cos(90-45)+695.1cos(45) is (10661sqrt(2))/(20)