What is the general solution for csc(2x+3)= 5/4 ?

The general solution for csc(2x+3)= 5/4 is x=180n-1.5+(0.92729…)/2 ,x=180n+90-1.5-(0.92729…)/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc(2x+3)= 5/4

Solution

csc (2 x + 3^{\circ}) = \frac{5}{4}

Solution

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

Radians

x = - \frac{π}{120} + \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{π}{120} - \frac{0.92729 \dots}{2} + πn

Solution steps

csc (2 x + 3^{\circ}) = \frac{5}{4}

Apply trig inverse properties

csc (2 x + 3^{\circ}) = \frac{5}{4}

General solutions for

csc (2 x + 3^{\circ}) = \frac{5}{4}

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

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n, 2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Solve

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

Move

3^{\circ}

to the right side

2 x + 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n

Subtract

3^{\circ}

from both sides

2 x + 3^{\circ} - 3^{\circ} = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Simplify

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Divide both sides by

2

2 x = arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Divide both sides by

2

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Group like terms

= \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} + \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{60 \cdot 2}

Multiply the numbers:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}

Solve

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Move

3^{\circ}

to the right side

2 x + 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n

Subtract

3^{\circ}

from both sides

2 x + 3^{\circ} - 3^{\circ} = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Simplify

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Divide both sides by

2

2 x = 18 0^{\circ} - arccsc (\frac{5}{4}) + 36 0^{\circ} n - 3^{\circ}

Divide both sides by

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Simplify

\frac{2 x}{2} = 9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

9 0^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2}

Group like terms

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} - \frac{3 ^{\circ}}{2} - \frac{arccsc ( \frac{5}{4} )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Divide the numbers:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 ^{\circ}}{2} = 1. 5^{\circ}

\frac{3 ^{\circ}}{2}

Apply the fraction rule:

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

= \frac{18 0 ^{\circ}}{60 \cdot 2}

Multiply the numbers:

60 \cdot 2 = 120

= 1. 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

Group like terms

= 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{arccsc ( \frac{5}{4} )}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{arccsc ( \frac{5}{4} )}{2}

Show solutions in decimal form

x = 18 0^{\circ} n - 1. 5^{\circ} + \frac{0.92729 \dots}{2}, x = 18 0^{\circ} n + 9 0^{\circ} - 1. 5^{\circ} - \frac{0.92729 \dots}{2}

Popular Examples

4cos^2(θ)-cos(θ)-9=7cos(θ)-4

4 cos^{2} (θ) - cos (θ) - 9 = 7 cos (θ) - 4

-sqrt(2)sin(2x)=sin^2(x)+cos^2(x)

- 2 sin (2 x) = sin^{2} (x) + cos^{2} (x)

cos(x)=0.998482

cos (x) = 0.998482

3sin(2x)-sin(x)=0

3 sin (2 x) - sin (x) = 0

(-6cos(x)-5sin(x))^2+11sin^2(x)=51

(- 6 cos (x) - 5 sin (x))^{2} + 11 sin^{2} (x) = 51

Frequently Asked Questions (FAQ)

What is the general solution for csc(2x+3)= 5/4 ?
The general solution for csc(2x+3)= 5/4 is x=180n-1.5+(0.92729…)/2 ,x=180n+90-1.5-(0.92729…)/2