Trigonometry Examples

y = sec (x)

$y = \sec (x)$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = sec (x)

$0 = \sec (x)$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as

sec (x) = 0

$\sec (x) = 0$ .

sec (x) = 0

$\sec (x) = 0$

Step 1.2.2

The range of secant is

y \leq - 1

$y \leq - 1$ and

y \geq 1

$y \geq 1$ . Since

0

$0$ does not fall in this range, there is no solution.

No solution

No solution

Step 1.3

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

x-intercept(s):

None

$None$

x-intercept(s):

None

$None$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = sec (0)

$y = \sec (0)$

Step 2.2

Solve the equation.

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Step 2.2.1

Remove parentheses.

y = sec (0)

$y = \sec (0)$

Step 2.2.2

The exact value of

sec (0)

$\sec (0)$ is

1

$1$ .

y = 1

$y = 1$

y = 1

$y = 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, 1)

$(0, 1)$

y-intercept(s):

(0, 1)

$(0, 1)$

Step 3

List the intersections.

x-intercept(s):

None

$None$

y-intercept(s):

(0, 1)

$(0, 1)$

Step 4

$y = \sec x$

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$