What is the value of 60cos(45)-70sin(60)-50sin(45) ?

The value of 60cos(45)-70sin(60)-50sin(45) is 5sqrt(2)-35sqrt(3)

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60cos(45)-70sin(60)-50sin(45)

60 cos (4 5^{\circ}) - 70 sin (6 0^{\circ}) - 50 sin (4 5^{\circ})

52 - 353

Decimal Notation

- 53.55071 \dots

Solution steps

60 cos (4 5^{\circ}) - 70 sin (6 0^{\circ}) - 50 sin (4 5^{\circ})

Use the following trivial identity:

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

cos (4 5^{\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{2}{2}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{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}

= 60 \cdot \frac{2}{2} - 70 \cdot \frac{3}{2} - 50 \cdot \frac{2}{2}

Simplify

60 \cdot \frac{2}{2} - 70 \cdot \frac{3}{2} - 50 \cdot \frac{2}{2} : 52 - 353

60 \cdot \frac{2}{2} - 70 \cdot \frac{3}{2} - 50 \cdot \frac{2}{2}

Group like terms

= 60 \cdot \frac{2}{2} - 50 \cdot \frac{2}{2} - 70 \cdot \frac{3}{2}

Add similar elements:

60 \cdot \frac{2}{2} - 50 \cdot \frac{2}{2} = 10 \cdot \frac{2}{2}

= 10 \cdot \frac{2}{2} - 70 \cdot \frac{3}{2}

10 \cdot \frac{2}{2} = 52

10 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 10}{2}

Divide the numbers:

\frac{10}{2} = 5

= 52

70 \cdot \frac{3}{2} = 353

70 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 70}{2}

Divide the numbers:

\frac{70}{2} = 35

= 353

= 52 - 353

= 52 - 353

tan^{2} (6 0^{\circ}) - 3 cot^{2} (6 0^{\circ})

20 \cdot sin (2 5^{\circ})

5.9 tan (5 9^{\circ})

- \frac{cos ( - 2 + 2 )}{2}

\frac{1}{sinh ( 0 )}

What is the value of 60cos(45)-70sin(60)-50sin(45) ?
The value of 60cos(45)-70sin(60)-50sin(45) is 5sqrt(2)-35sqrt(3)