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Popular >

solvefor θ,r=-3/(rcos(θ))

Solution

solve for

θ, r = - \frac{3}{r cos ( θ )}

Solution

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

Solution steps

r = - \frac{3}{r cos ( θ )}

Switch sides

- \frac{3}{r cos ( θ )} = r

Multiply both sides by

cos (θ)

- \frac{3}{r cos ( θ )} = r

Multiply both sides by

cos (θ)

- \frac{3}{r cos ( θ )} cos (θ) = r cos (θ)

Simplify

- \frac{3}{r} = r cos (θ)

- \frac{3}{r} = r cos (θ)

Switch sides

r cos (θ) = - \frac{3}{r}

Divide both sides by

r; r \neq = 0

r cos (θ) = - \frac{3}{r}

Divide both sides by

r; r \neq = 0

\frac{r cos ( θ )}{r} = \frac{- \frac{3}{r}}{r}; r \neq = 0

Simplify

\frac{r cos ( θ )}{r} = \frac{- \frac{3}{r}}{r}

Simplify

\frac{r cos ( θ )}{r} : cos (θ)

\frac{r cos ( θ )}{r}

Cancel the common factor:

r

= cos (θ)

Simplify

\frac{- \frac{3}{r}}{r} : - \frac{3}{r ^{2}}

\frac{- \frac{3}{r}}{r}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{3}{r}}{r}

Apply the fraction rule:

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

\frac{\frac{3}{r}}{r} = \frac{3}{rr}

= - \frac{3}{rr}

rr = r^{2}

rr

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

rr = r^{1 + 1}

= r^{1 + 1}

Add the numbers:

1 + 1 = 2

= r^{2}

= - \frac{3}{r ^{2}}

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

cos (θ) = - \frac{3}{r ^{2}}; r \neq = 0

Apply trig inverse properties

cos (θ) = - \frac{3}{r ^{2}}

General solutions for

cos (θ) = - \frac{3}{r ^{2}}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

θ = arccos (- \frac{3}{r ^{2}}) + 2 πn, θ = - arccos (- \frac{3}{r ^{2}}) + 2 πn

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