Solve for θ in Degrees 16sec(theta)^2-1=0

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Trigonometry

$16 \sec^{2} (θ) - 1 = 0$

Add $1$ to both sides of the equation.

$16 \sec^{2} (θ) = 1$

Divide each term in $16 \sec^{2} (θ) = 1$ by $16$ and simplify.

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Divide each term in $16 \sec^{2} (θ) = 1$ by $16$ .

$\frac{16 \sec^{2} (θ)}{16} = \frac{1}{16}$

Simplify the left side.

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Cancel the common factor of $16$ .

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Cancel the common factor.

$\frac{16 \sec^{2} (θ)}{16} = \frac{1}{16}$

Divide $\sec^{2} (θ)$ by $1$ .

$\sec^{2} (θ) = \frac{1}{16}$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$\sec (θ) = \pm \sqrt{\frac{1}{16}}$

Simplify $\pm \sqrt{\frac{1}{16}}$ .

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Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

$\sec (θ) = \pm \frac{\sqrt{1}}{\sqrt{16}}$

Any root of $1$ is $1$ .

$\sec (θ) = \pm \frac{1}{\sqrt{16}}$

Simplify the denominator.

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Rewrite $16$ as $4^{2}$ .

$\sec (θ) = \pm \frac{1}{\sqrt{4^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\sec (θ) = \pm \frac{1}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

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First, use the positive value of the $\pm$ to find the first solution.

$\sec (θ) = \frac{1}{4}$

Next, use the negative value of the $\pm$ to find the second solution.

$\sec (θ) = - \frac{1}{4}$

The complete solution is the result of both the positive and negative portions of the solution.

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

Set up each of the solutions to solve for $θ$ .

$\sec (θ) = \frac{1}{4}$

$\sec (θ) = - \frac{1}{4}$

Solve for $θ$ in $\sec (θ) = \frac{1}{4}$ .

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The range of secant is $y \leq - 1$ and $y \geq 1$ . Since $\frac{1}{4}$ does not fall in this range, there is no solution.

No solution

Solve for $θ$ in $\sec (θ) = - \frac{1}{4}$ .

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The range of secant is $y \leq - 1$ and $y \geq 1$ . Since $- \frac{1}{4}$ does not fall in this range, there is no solution.

No solution

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Name

Name	six hundred ninety-eight million eighty thousand seven hundred eighty-four

Interesting facts

698080784 has 32 divisors, whose sum is 3534034050
The reverse of 698080784 is 487080896
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 50
Digital Root 5

Name

Name	seven hundred one million eight hundred seventy thousand

Interesting facts

701870000 has 128 divisors, whose sum is 4267274400
The reverse of 701870000 is 000078107
Previous prime number is 1625

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 23
Digital Root 5

Name

Name	one billion four hundred seventy million four hundred thirty-six thousand eight hundred eighty-four

Interesting facts

1470436884 has 128 divisors, whose sum is 5487390720
The reverse of 1470436884 is 4886340741
Previous prime number is 7

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 45
Digital Root 9

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