What is the value of sin(30)+(sin(45))(sin(45))-1 ?

The value of sin(30)+(sin(45))(sin(45))-1 is 0

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sin(30)+(sin(45))(sin(45))-1

sin (3 0^{\circ}) + (sin (4 5^{\circ})) (sin (4 5^{\circ})) - 1

0

Solution steps

sin (3 0^{\circ}) + (sin (4 5^{\circ})) (sin (4 5^{\circ})) - 1

= sin (3 0^{\circ}) + sin (4 5^{\circ}) sin (4 5^{\circ}) - 1

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}

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

Simplify

\frac{1}{2} + \frac{2}{2} \cdot \frac{2}{2} - 1 : 0

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

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

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

Multiply fractions:

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

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

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{2}{4}

Cancel the common factor:

2

= \frac{1}{2}

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

Combine the fractions

\frac{1}{2} + \frac{1}{2} : 1

Apply rule

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

= \frac{1 + 1}{2}

Add the numbers:

1 + 1 = 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1 - 1

Subtract the numbers:

1 - 1 = 0

= 0

= 0

2 \cdot 9.81 \cdot 3.5 \cdot cos (5 0^{\circ})

sin (25 0^{\circ}) cos (1 0^{\circ}) - cos (25 0^{\circ}) sin (1 0^{\circ})

arctan (\frac{- 2}{2})

csc (8 3^{\circ})

cos (1.3 π)

What is the value of sin(30)+(sin(45))(sin(45))-1 ?
The value of sin(30)+(sin(45))(sin(45))-1 is 0