What is the general solution for (11.0994)/(cos(x))=(3.5355)/(sin(x)) ?

The general solution for (11.0994)/(cos(x))=(3.5355)/(sin(x)) is x=0.30836…+pin

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Popular >

(11.0994)/(cos(x))=(3.5355)/(sin(x))

Solution

\frac{11.0994}{cos ( x )} = \frac{3.5355}{sin ( x )}

Solution

x = 0.30836 \dots + πn

Degrees

x = 17.66827 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{11.0994}{cos ( x )} = \frac{3.5355}{sin ( x )}

Subtract

\frac{3.5355}{sin ( x )}

from both sides

\frac{11.0994}{cos ( x )} - \frac{3.5355}{sin ( x )} = 0

Simplify

\frac{11.0994}{cos ( x )} - \frac{3.5355}{sin ( x )} : \frac{11.0994 sin ( x ) - 3.5355 cos ( x )}{cos ( x ) sin ( x )}

\frac{11.0994}{cos ( x )} - \frac{3.5355}{sin ( x )}

Least Common Multiplier of

cos (x), sin (x) : cos (x) sin (x)

cos (x), sin (x)

Lowest Common Multiplier (LCM)

Compute an expression comprised of factors that appear either in

cos (x)

sin (x)

= cos (x) sin (x)

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

cos (x) sin (x)

For

\frac{11.0994}{cos ( x )} :

multiply the denominator and numerator by

sin (x)

\frac{11.0994}{cos ( x )} = \frac{11.0994 sin ( x )}{cos ( x ) sin ( x )}

For

\frac{3.5355}{sin ( x )} :

multiply the denominator and numerator by

cos (x)

\frac{3.5355}{sin ( x )} = \frac{3.5355 cos ( x )}{sin ( x ) cos ( x )}

= \frac{11.0994 sin ( x )}{cos ( x ) sin ( x )} - \frac{3.5355 cos ( x )}{sin ( x ) cos ( x )}

Since the denominators are equal, combine the fractions:

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

= \frac{11.0994 sin ( x ) - 3.5355 cos ( x )}{cos ( x ) sin ( x )}

\frac{11.0994 sin ( x ) - 3.5355 cos ( x )}{cos ( x ) sin ( x )} = 0

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

11.0994 sin (x) - 3.5355 cos (x) = 0

Rewrite using trig identities

11.0994 sin (x) - 3.5355 cos (x) = 0

Divide both sides by

cos (x), cos (x) \neq = 0

\frac{11.0994 sin ( x ) - 3.5355 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{11.0994 sin ( x )}{cos ( x )} - 3.5355 = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

11.0994 tan (x) - 3.5355 = 0

11.0994 tan (x) - 3.5355 = 0

Move

3.5355

to the right side

11.0994 tan (x) - 3.5355 = 0

Add

3.5355

to both sides

11.0994 tan (x) - 3.5355 + 3.5355 = 0 + 3.5355

Simplify

11.0994 tan (x) = 3.5355

11.0994 tan (x) = 3.5355

Divide both sides by

11.0994

11.0994 tan (x) = 3.5355

Divide both sides by

11.0994

\frac{11.0994 tan ( x )}{11.0994} = \frac{3.5355}{11.0994}

Simplify

tan (x) = \frac{3.5355}{11.0994}

tan (x) = \frac{3.5355}{11.0994}

Apply trig inverse properties

tan (x) = \frac{3.5355}{11.0994}

General solutions for

tan (x) = \frac{3.5355}{11.0994}

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (\frac{3.5355}{11.0994}) + πn

x = arctan (\frac{3.5355}{11.0994}) + πn

Show solutions in decimal form

x = 0.30836 \dots + πn

Popular Examples

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(\frac{sec ( x )}{cos ( x )})^{2} = tan^{2} (x)

sin(x/2)-cos(x/2)=0

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

cos^2(x)+sin^2(x)=sin(x)+1/2

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

sin(A)=0.53

sin (A) = 0.53

Frequently Asked Questions (FAQ)

What is the general solution for (11.0994)/(cos(x))=(3.5355)/(sin(x)) ?
The general solution for (11.0994)/(cos(x))=(3.5355)/(sin(x)) is x=0.30836…+pin