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Popular >

-3sqrt(3)+7csc(θ/5+23)=5sqrt(3)

Solution

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

Solution

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

Radians

θ = 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn, θ = 5 π - 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn

Solution steps

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

Move

33

to the right side

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

Add

33

to both sides

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

Simplify

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

Simplify

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 : 7 csc (\frac{θ}{5} + 2 3^{\circ})

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33

Add similar elements:

- 33 + 33 = 0

= 7 csc (\frac{θ}{5} + 2 3^{\circ})

Simplify

53 + 33 : 83

53 + 33

Add similar elements:

53 + 33 = 83

= 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

Divide both sides by

7

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

Divide both sides by

7

\frac{7 csc ( \frac{θ}{5} + 2 3 ^{\circ} )}{7} = \frac{8 3}{7}

Simplify

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

Apply trig inverse properties

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

General solutions for

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Solve

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Move

2 3^{\circ}

to the right side

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Subtract

2 3^{\circ}

from both sides

\frac{θ}{5} + 2 3^{\circ} - 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Simplify

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Multiply both sides by

5

\frac{θ}{5} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Multiply both sides by

5

\frac{5 θ}{5} = 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

Simplify

\frac{5 θ}{5} = 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

Simplify

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Divide the numbers:

\frac{5}{5} = 1

= θ

Simplify

5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ} : 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

Multiply the numbers:

5 \cdot 2 = 10

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

Multiply fractions:

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

= 11 5^{\circ}

Multiply the numbers:

23 \cdot 5 = 115

= 11 5^{\circ}

Cancel the common factor:

5

= 11 5^{\circ}

= 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

Solve

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Move

2 3^{\circ}

to the right side

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

Subtract

2 3^{\circ}

from both sides

\frac{θ}{5} + 2 3^{\circ} - 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Simplify

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Multiply both sides by

5

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

Multiply both sides by

5

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

Simplify

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

Simplify

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

Divide the numbers:

\frac{5}{5} = 1

= θ

Simplify

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ} : 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

Multiply the numbers:

5 \cdot 2 = 10

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

Multiply fractions:

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

= 11 5^{\circ}

Multiply the numbers:

23 \cdot 5 = 115

= 11 5^{\circ}

Cancel the common factor:

5

= 11 5^{\circ}

= 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

Show solutions in decimal form

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

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