What is the general solution for cos(90-x)+csc(x)= 5/2 ?

The general solution for cos(90-x)+csc(x)= 5/2 is x=30+360n,x=150+360n

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(90-x)+csc(x)= 5/2

cos (9 0^{\circ} - x) + csc (x) = \frac{5}{2}

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

Solution steps

cos (9 0^{\circ} - x) + csc (x) = \frac{5}{2}

Rewrite using trig identities

sin (x) + csc (x) = \frac{5}{2}

Subtract

\frac{5}{2}

from both sides

sin (x) + csc (x) - \frac{5}{2} = 0

Simplify

sin (x) + csc (x) - \frac{5}{2} : \frac{2 sin ( x ) + 2 csc ( x ) - 5}{2}

\frac{2 sin ( x ) + 2 csc ( x ) - 5}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 sin (x) + 2 csc (x) - 5 = 0

Rewrite using trig identities

- 5 + \frac{2}{csc ( x )} + 2 csc (x) = 0

Solve by substitution

csc (x) = 2, csc (x) = \frac{1}{2}

csc (x) = 2 : x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

csc (x) = \frac{1}{2} :

No Solution

Combine all the solutions

x = 3 0^{\circ} + 36 0^{\circ} n, x = 15 0^{\circ} + 36 0^{\circ} n

x, sin (x) - csc (t) + 1 = 0

cos^{2} (x) = \frac{3}{4 \cdot 5 cos ^{2} ( x )}

\frac{cos ^{2} ( x )}{1 - cos ( x )} = 1 + cos (x)

sin (x) = \frac{19}{50}

5 sin (2 x - \frac{π}{2}) = 0.5

What is the general solution for cos(90-x)+csc(x)= 5/2 ?
The general solution for cos(90-x)+csc(x)= 5/2 is x=30+360n,x=150+360n