What is the value of 2sin(30)+3cos(60)-3tan(45) ?

The value of 2sin(30)+3cos(60)-3tan(45) is -1/2

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2sin(30)+3cos(60)-3tan(45)

2 sin (3 0^{\circ}) + 3 cos (6 0^{\circ}) - 3 tan (4 5^{\circ})

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

2 sin (3 0^{\circ}) + 3 cos (6 0^{\circ}) - 3 tan (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:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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{1}{2}

Use the following trivial identity:

tan (4 5^{\circ}) = 1

tan (4 5^{\circ})

tan (x)

periodicity table with

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= 2 \cdot \frac{1}{2} + 3 \cdot \frac{1}{2} - 3 \cdot 1

Simplify

2 \cdot \frac{1}{2} + 3 \cdot \frac{1}{2} - 3 \cdot 1 : - \frac{1}{2}

2 \cdot \frac{1}{2} + 3 \cdot \frac{1}{2} - 3 \cdot 1

Add similar elements:

2 \cdot \frac{1}{2} + 3 \cdot \frac{1}{2} = 5 \cdot \frac{1}{2}

= 5 \cdot \frac{1}{2} - 3 \cdot 1

5 \cdot \frac{1}{2} = \frac{5}{2}

5 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 5}{2}

Multiply the numbers:

1 \cdot 5 = 5

= \frac{5}{2}

3 \cdot 1 = 3

3 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= 3

= \frac{5}{2} - 3

Convert element to fraction:

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

= - \frac{3 \cdot 2}{2} + \frac{5}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 \cdot 2 + 5}{2}

- 3 \cdot 2 + 5 = - 1

- 3 \cdot 2 + 5

Multiply the numbers:

3 \cdot 2 = 6

= - 6 + 5

Add/Subtract the numbers:

- 6 + 5 = - 1

= - 1

= \frac{- 1}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{2}

= - \frac{1}{2}

cos (arcsin (\frac{4}{5}) + arccos (\frac{3}{5}))

90 sin (6 0^{\circ})

cos (2) (90)

3 tan (4 5^{\circ})

tan (0.53)

What is the value of 2sin(30)+3cos(60)-3tan(45) ?
The value of 2sin(30)+3cos(60)-3tan(45) is -1/2