What is the value of csc(-600) ?

The value of csc(-600) is (2sqrt(3))/3

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Popular >

csc(-600)

Solution

csc (- 60 0^{\circ})

Solution

\frac{2 3}{3}

Decimal Notation

1.15470 \dots

Solution steps

csc (- 60 0^{\circ})

Use the following property:

csc (- x) = - csc (x)

csc (- 60 0^{\circ}) = - csc (60 0^{\circ})

= - csc (60 0^{\circ})

csc (60 0^{\circ}) = csc (24 0^{\circ})

csc (60 0^{\circ})

Rewrite

60 0^{\circ}

36 0^{\circ} + 24 0^{\circ}

= csc (36 0^{\circ} + 24 0^{\circ})

Apply the periodicity of

csc

csc (x + 36 0^{\circ}) = csc (x)

csc (36 0^{\circ} + 24 0^{\circ}) = csc (24 0^{\circ})

= csc (24 0^{\circ})

= - csc (24 0^{\circ})

Rewrite using trig identities:

csc (24 0^{\circ}) = - \frac{2 3}{3}

csc (24 0^{\circ})

Rewrite using trig identities:

\frac{1}{sin ( 24 0 ^{\circ} )}

csc (24 0^{\circ})

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

= \frac{1}{sin ( 24 0 ^{\circ} )}

= \frac{1}{sin ( 24 0 ^{\circ} )}

Rewrite using trig identities:

sin (24 0^{\circ}) = - \frac{3}{2}

sin (24 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (6 0^{\circ}) + cos (18 0^{\circ}) sin (6 0^{\circ})

sin (24 0^{\circ})

Write

sin (24 0^{\circ})

sin (18 0^{\circ} + 6 0^{\circ})

= sin (18 0^{\circ} + 6 0^{\circ})

Use the Angle Sum identity:

sin (s + t) = sin (s) cos (t) + cos (s) sin (t)

= sin (18 0^{\circ}) cos (6 0^{\circ}) + cos (18 0^{\circ}) sin (6 0^{\circ})

= sin (18 0^{\circ}) cos (6 0^{\circ}) + cos (18 0^{\circ}) sin (6 0^{\circ})

Use the following trivial identity:

sin (18 0^{\circ}) = 0

sin (18 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}

= 0

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:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

Use the following trivial identity:

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

sin (6 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{3}{2}

= 0 \cdot \frac{1}{2} + (- 1) \frac{3}{2}

Simplify

= - \frac{3}{2}

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

Simplify

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

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

Apply the fraction rule:

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

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

= - \frac{2}{3}

Rationalize

- \frac{2}{3} : - \frac{2 3}{3}

- \frac{2}{3}

Multiply by the conjugate

\frac{3}{3}

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

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

= - \frac{2 3}{3}

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

Simplify

= \frac{2 3}{3}

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Frequently Asked Questions (FAQ)

What is the value of csc(-600) ?
The value of csc(-600) is (2sqrt(3))/3