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

The value of (tan(60)sin(30))/(cos(60)) is square root of 3

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(tan(60)sin(30))/(cos(60))

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

3

Decimal Notation

1.73205 \dots

Solution steps

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

Use the following trivial identity:

tan (6 0^{\circ}) = 3

tan (6 0^{\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}

= 3

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}

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

Simplify

\frac{3 \frac{1}{2}}{\frac{1}{2}} : 3

\frac{3 \frac{1}{2}}{\frac{1}{2}}

Apply the fraction rule:

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

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

Apply the fraction rule:

\frac{a}{1} = a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 1 \cdot 3

Multiply:

1 \cdot 3 = 3

= 3

= 3

- sin (\frac{7 π}{2})

\frac{1 - cos ( - 0.1 )}{- 0.1}

cos (56.3 1^{\circ})

cos (28 5^{\circ}) - cos (16 5^{\circ})

arcsin (\frac{5}{2})

What is the value of (tan(60)sin(30))/(cos(60)) ?
The value of (tan(60)sin(30))/(cos(60)) is square root of 3