Trigonometry Examples

$\cos (x) (2 \sin (x) + \sqrt{2}) = 0$

Step 1

Simplify $\cos (x) (2 \sin (x) + \sqrt{2})$ .

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Step 1.1

Simplify by multiplying through.

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Step 1.1.1

Apply the distributive property.

$\cos (x) (2 \sin (x)) + \cos (x) \sqrt{2} = 0$

Step 1.1.2

Rewrite using the commutative property of multiplication.

$2 \cos (x) \sin (x) + \cos (x) \sqrt{2} = 0$

Step 1.2

Simplify each term.

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Step 1.2.1

Reorder $2 \cos (x)$ and $\sin (x)$ .

$\sin (x) (2 \cos (x)) + \cos (x) \sqrt{2} = 0$

Step 1.2.2

Reorder $\sin (x)$ and $2$ .

$2 \cdot \sin (x) \cos (x) + \cos (x) \sqrt{2} = 0$

Step 1.2.3

Apply the sine double-angle identity.

$\sin (2 x) + \cos (x) \sqrt{2} = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = \frac{π}{2} + 2 π n, \frac{5 π}{4} + 2 π n, \frac{3 π}{2} + 2 π n, \frac{7 π}{4} + 2 π n$ , for any integer $n$

Step 3