What is the value of (cos(60)*3)-(sin(60)*5) ?

The value of (cos(60)*3)-(sin(60)*5) is (3-5sqrt(3))/2

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(cos(60)3)-(sin(60)5)

(cos (6 0^{\circ}) \cdot 3) - (sin (6 0^{\circ}) \cdot 5)

\frac{3 - 5 3}{2}

Decimal Notation

- 2.83012 \dots

Solution steps

(cos (6 0^{\circ}) \cdot 3) - (sin (6 0^{\circ}) \cdot 5)

= cos (6 0^{\circ}) \cdot 3 - sin (6 0^{\circ}) \cdot 5

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:

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}

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

Simplify

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

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

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

\frac{1}{2} \cdot 3

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 3 = 3

= \frac{3}{2}

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

\frac{3}{2} \cdot 5

Multiply fractions:

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

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

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

Apply rule

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

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

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

sin (31 5^{\circ} - 3 0^{\circ})

cot (arcsec (17))

31 cos (4 5^{\circ})

sec (49.9 6^{\circ})

tan (arccos (\frac{7}{11}))

What is the value of (cos(60)*3)-(sin(60)*5) ?
The value of (cos(60)*3)-(sin(60)*5) is (3-5sqrt(3))/2