What is the general solution for 16sec^2(θ)-1=0 ?

The general solution for 16sec^2(θ)-1=0 is No Solution for θ\in\mathbb{R}

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Popular Trigonometry >

16sec^2(θ)-1=0

Solution

16 sec^{2} (θ) - 1 = 0

Solution

No Solution for θ \in R

Solution steps

16 sec^{2} (θ) - 1 = 0

Solve by substitution

16 sec^{2} (θ) - 1 = 0

Let:

sec (θ) = u

16 u^{2} - 1 = 0

16 u^{2} - 1 = 0 : u = \frac{1}{4}, u = - \frac{1}{4}

16 u^{2} - 1 = 0

Move

1

to the right side

16 u^{2} - 1 = 0

Add

1

to both sides

16 u^{2} - 1 + 1 = 0 + 1

Simplify

16 u^{2} = 1

16 u^{2} = 1

Divide both sides by

16

16 u^{2} = 1

Divide both sides by

16

\frac{16 u ^{2}}{16} = \frac{1}{16}

Simplify

u^{2} = \frac{1}{16}

u^{2} = \frac{1}{16}

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = \frac{1}{16}, u = - \frac{1}{16}

\frac{1}{16} = \frac{1}{4}

\frac{1}{16}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{1}{16}

16 = 4

16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

n a^{n} = a

4^{2} = 4

= 4

= \frac{1}{4}

Apply rule

1 = 1

= \frac{1}{4}

- \frac{1}{16} = - \frac{1}{4}

- \frac{1}{16}

Simplify

\frac{1}{16} : \frac{1}{4}

\frac{1}{16}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{1}{16}

16 = 4

16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

n a^{n} = a

4^{2} = 4

= 4

= \frac{1}{4}

= - \frac{1}{4}

Apply rule

1 = 1

= - \frac{1}{4}

u = \frac{1}{4}, u = - \frac{1}{4}

Substitute back

u = sec (θ)

sec (θ) = \frac{1}{4}, sec (θ) = - \frac{1}{4}

sec (θ) = \frac{1}{4}, sec (θ) = - \frac{1}{4}

sec (θ) = \frac{1}{4} :

No Solution

sec (θ) = \frac{1}{4}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

sec (θ) = - \frac{1}{4} :

No Solution

sec (θ) = - \frac{1}{4}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

No Solution for θ \in R

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 16sec^2(θ)-1=0 ?
The general solution for 16sec^2(θ)-1=0 is No Solution for θ\in\mathbb{R}