What is the value of csc(pi/3)+sin(-30) ?

The value of csc(pi/3)+sin(-30) is (2sqrt(3))/3-1/2

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csc(pi/3)+sin(-30)

csc (\frac{π}{3}) + sin (- 3 0^{\circ})

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

Decimal Notation

0.65470 \dots

Solution steps

csc (6 0^{\circ}) + sin (- 3 0^{\circ})

Use the following trivial identity:

csc (6 0^{\circ}) = \frac{2 3}{3}

csc (6 0^{\circ})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

Rewrite using trig identities:

sin (- 3 0^{\circ}) = - \frac{1}{2}

sin (- 3 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 3 0^{\circ}) = - sin (3 0^{\circ})

= - sin (3 0^{\circ})

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{1}{2}

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

arctan (- \frac{3}{2}) + π

\frac{1}{cos ^{2} ( \frac{2 π}{3} )}

3 sin (18 0^{\circ})

90 tan (4 4^{\circ})

sin (\frac{\frac{3}{2} + 1}{2})

What is the value of csc(pi/3)+sin(-30) ?
The value of csc(pi/3)+sin(-30) is (2sqrt(3))/3-1/2