What is the value of 2sin(45)+4cos(30) ?

The value of 2sin(45)+4cos(30) is sqrt(2)+2sqrt(3)

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2sin(45)+4cos(30)

2 sin (4 5^{\circ}) + 4 cos (3 0^{\circ})

2 + 23

Decimal Notation

4.87831 \dots

Solution steps

2 sin (4 5^{\circ}) + 4 cos (3 0^{\circ})

Use the following trivial identity:

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

sin (4 5^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} 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 (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\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{3}{2}

= 2 \cdot \frac{2}{2} + 4 \cdot \frac{3}{2}

Simplify

2 \cdot \frac{2}{2} + 4 \cdot \frac{3}{2} : 2 + 23

2 \cdot \frac{2}{2} + 4 \cdot \frac{3}{2}

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

2 \cdot \frac{2}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 2

4 \cdot \frac{3}{2} = 23

4 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 23

= 2 + 23

= 2 + 23

5 sin (32 0^{\circ}) + 4 sin (25 0^{\circ})

cos (0.322)

- π sin (0)

arcsec (\frac{3}{2})

4 + 9 + 2 (2) (3) cos (5 6^{\circ})

What is the value of 2sin(45)+4cos(30) ?
The value of 2sin(45)+4cos(30) is sqrt(2)+2sqrt(3)