Trigonometry Examples

$y = \cos (x) - 2$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \cos (x) - 2$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Rewrite the equation as $\cos (x) - 2 = 0$ .

$\cos (x) - 2 = 0$

Step 1.2.2

Add $2$ to both sides of the equation.

$\cos (x) = 2$

Step 1.2.3

The range of cosine is $- 1 \leq y \leq 1$ . Since $2$ does not fall in this range, there is no solution.

No solution

Step 1.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \cos (0) - 2$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = \cos (0) - 2$

Step 2.2.2

Simplify $\cos (0) - 2$ .

Tap for more steps...

Step 2.2.2.1

The exact value of $\cos (0)$ is $1$ .

$y = 1 - 2$

Step 2.2.2.2

Subtract $2$ from $1$ .

$y = - 1$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - 1)$

Step 4