Trigonometry Examples

$\sin (0) < 0$ , $\cos (0) > 0$

Step 1

Solve $\sin (0) < 0$ for .

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Step 1.1

The exact value of $\sin (0)$ is $0$ .

$0 < 0$

Step 1.2

The inequality is never true.

No solution

Step 1.3

Identify the leading coefficient.

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Step 1.3.1

The exact value of $\sin (0)$ is $0$ .

$0$

Step 1.3.2

The leading term in a polynomial is the term with the highest degree.

$0$

Step 1.3.3

The leading coefficient in a polynomial is the coefficient of the leading term.

$0$

Step 1.4

Since there are no real x-intercepts and the leading coefficient is positive, the parabola opens up and $\sin (0)$ is always greater than $0$ .

No solution

Step 2

Solve $\cos (0) > 0$ for .

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Step 2.1

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

$1 > 0$

Step 2.2

Since $1 > 0$ , the inequality will always be true.

Always true

Step 3

Find the intersection.

No solution