What is the value of tan(pi/3)+cos((5pi)/6)*sin(-(3pi)/4) ?

The value of tan(pi/3)+cos((5pi)/6)*sin(-(3pi)/4) is sqrt(3)+(sqrt(6))/4

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tan(pi/3)+cos((5pi)/6)*sin(-(3pi)/4)

tan (\frac{π}{3}) + cos (\frac{5 π}{6}) \cdot sin (- \frac{3 π}{4})

3 + \frac{6}{4}

Decimal Notation

2.34442 \dots

Solution steps

tan (\frac{π}{3}) + cos (\frac{5 π}{6}) sin (- \frac{3 π}{4})

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 π}{6})

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}

= - \frac{3}{2}

Rewrite using trig identities:

sin (- \frac{3 π}{4}) = - \frac{2}{2}

sin (- \frac{3 π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{3 π}{4}) = - sin (\frac{3 π}{4})

= - sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

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}

= \frac{2}{2}

= - \frac{2}{2}

= 3 + (- \frac{3}{2}) (- \frac{2}{2})

Simplify

3 + (- \frac{3}{2}) (- \frac{2}{2}) : 3 + \frac{6}{4}

3 + (- \frac{3}{2}) (- \frac{2}{2})

Remove parentheses:

(- a) = - a, - (- a) = a

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

\frac{3}{2} \cdot \frac{2}{2} = \frac{6}{4}

\frac{3}{2} \cdot \frac{2}{2}

Multiply fractions:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3 2}{4}

Simplify

32 : 6

32

Apply radical rule:

a b = a \cdot b

32 = 3 \cdot 2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

= \frac{6}{4}

= 3 + \frac{6}{4}

= 3 + \frac{6}{4}

cos^{2} (6 7^{\circ})

sin (2 π) - sin (0)

csc (- \frac{13 π}{4})

cot (87 0^{\circ})

arccsc (sin (\frac{π}{6}))

What is the value of tan(pi/3)+cos((5pi)/6)*sin(-(3pi)/4) ?
The value of tan(pi/3)+cos((5pi)/6)*sin(-(3pi)/4) is sqrt(3)+(sqrt(6))/4