en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

solvefor x,y=sqrt(r(sec(x)))

Solution

solve for

x, y = r (sec (x))

Solution

x = arcsec (\frac{y ^{2}}{r}) + 2 πn, x = - arcsec (\frac{y ^{2}}{r}) + 2 πn

Solution steps

y = r (sec (x))

Switch sides

r sec (x) = y

Square both sides:

r sec (x) = y^{2}

r sec (x) = y

(r sec (x))^{2} = y^{2}

Expand

(r sec (x))^{2} : r sec (x)

(r sec (x))^{2}

Apply radical rule:

a = a^{\frac{1}{2}}

= ((r sec (x))^{\frac{1}{2}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (r sec (x))^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

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

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= r sec (x)

r sec (x) = y^{2}

r sec (x) = y^{2}

Solve

r sec (x) = y^{2} : sec (x) = \frac{y ^{2}}{r}

r sec (x) = y^{2}

Divide both sides by

r

r sec (x) = y^{2}

Divide both sides by

r

\frac{r sec ( x )}{r} = \frac{y ^{2}}{r}

Simplify

sec (x) = \frac{y ^{2}}{r}

sec (x) = \frac{y ^{2}}{r}

sec (x) = \frac{y ^{2}}{r}

Apply trig inverse properties

sec (x) = \frac{y ^{2}}{r}

General solutions for

sec (x) = \frac{y ^{2}}{r}

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

x = arcsec (\frac{y ^{2}}{r}) + 2 πn, x = - arcsec (\frac{y ^{2}}{r}) + 2 πn

x = arcsec (\frac{y ^{2}}{r}) + 2 πn, x = - arcsec (\frac{y ^{2}}{r}) + 2 πn

Popular Examples

csc^2(x)-3=6tan(x)

csc^{2} (x) - 3 = 6 tan (x)

solvefor C,arctan((1/(2*pi*R*C))/f)=0 solve for

C, arctan (\frac{\frac{1}{2 \cdot π \cdot R \cdot C}}{f}) = 0

sin(x)=-2cos(x)

sin (x) = - 2 cos (x)

3sin^2(x)-4cos(x)+1=0

3 sin^{2} (x) - 4 cos (x) + 1 = 0

sin(x)-cos(2x)-1=0

sin (x) - cos (2 x) - 1 = 0