What is the value of 2sin(30)-2sin(45) ?

The value of 2sin(30)-2sin(45) is 1-sqrt(2)

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2sin(30)-2sin(45)

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

1 - 2

Decimal Notation

- 0.41421 \dots

Solution steps

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

Use the following trivial identity:

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

sin (3 0^{\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{1}{2}

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 \cdot \frac{1}{2} - 2 \cdot \frac{2}{2}

Simplify

2 \cdot \frac{1}{2} - 2 \cdot \frac{2}{2} : 1 - 2

2 \cdot \frac{1}{2} - 2 \cdot \frac{2}{2}

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

2 \cdot \frac{1}{2}

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

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

= 1 - 2

= 1 - 2

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

arcsec (- \frac{3}{3})

arctan (\frac{14}{9})

cos^{2} (53.1 3^{\circ})

sec^{2} (9)

What is the value of 2sin(30)-2sin(45) ?
The value of 2sin(30)-2sin(45) is 1-sqrt(2)