What is the value of (3cos(pi))/(sin(pi)+6) ?

The value of (3cos(pi))/(sin(pi)+6) is -1/2

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(3cos(pi))/(sin(pi)+6)

\frac{3 cos ( π )}{sin ( π ) + 6}

- \frac{1}{2}

Decimal Notation

- 0.5

Solution steps

\frac{3 cos ( π )}{sin ( π ) + 6}

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= (- 1)

Use the following trivial identity:

sin (π) = 0

sin (π)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= \frac{3 ( - 1 )}{0 + 6}

Simplify

\frac{3 ( - 1 )}{0 + 6} : - \frac{1}{2}

\frac{3 ( - 1 )}{0 + 6}

Remove parentheses:

(- a) = - a

= \frac{- 3 \cdot 1}{0 + 6}

Multiply the numbers:

3 \cdot 1 = 3

= \frac{- 3}{0 + 6}

Add the numbers:

0 + 6 = 6

= \frac{- 3}{6}

Apply the fraction rule:

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

= - \frac{3}{6}

Cancel the common factor:

3

= - \frac{1}{2}

= - \frac{1}{2}

arccos (10)

2 sin (1 8^{\circ}) cos (1 8^{\circ})

arccsc (\frac{2}{2})

6.7 tan (3 4^{\circ})

2 cos^{2} (\frac{π}{4})

What is the value of (3cos(pi))/(sin(pi)+6) ?
The value of (3cos(pi))/(sin(pi)+6) is -1/2