What is the value of (cos(60)+sin(30))/4 ?

The value of (cos(60)+sin(30))/4 is 1/4

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(cos(60)+sin(30))/4

\frac{cos ( 6 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{4}

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\frac{cos ( 6 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{4}

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 (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}

= \frac{\frac{1}{2} + \frac{1}{2}}{4}

Simplify

\frac{\frac{1}{2} + \frac{1}{2}}{4} : \frac{1}{4}

\frac{\frac{1}{2} + \frac{1}{2}}{4}

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

= \frac{1}{4}

= \frac{1}{4}

\frac{100}{tan ( 4 0 ^{\circ} )}

sin (6 0^{\circ}) cos (6 0^{\circ}) tan (6 0^{\circ}) cot (6 0^{\circ}) sec (6 0^{\circ}) csc (6 0^{\circ})

arcsin (\frac{sin ( 35. 5 ^{\circ} )}{1.333})

10 sin (\frac{π}{6} 5)

4 sin (\frac{1}{4}) - cos (\frac{1}{4})

What is the value of (cos(60)+sin(30))/4 ?
The value of (cos(60)+sin(30))/4 is 1/4