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

The value of 2+2sin(45) is 2+sqrt(2)

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2+2sin(45)

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

2 + 2

Decimal Notation

3.41421 \dots

Solution steps

2 + 2 sin (4 5^{\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}

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

Simplify

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

2 + 2 \cdot \frac{2}{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

= 2 + 2

= 2 + 2

csc (1 7^{\circ})

arccos (0.991)

cos^{2} (62.0 8^{\circ})

16 \cdot sin (4 5^{\circ})

arccos (0.995)