Trigonometry Examples

$2 \cos^{2} (\frac{π}{2}) + \sin (\frac{π}{2}) - 1$

Step 1

Move $- 1$ .

$2 \cos^{2} (\frac{π}{2}) - 1 + \sin (\frac{π}{2})$

Step 2

Apply the cosine double-angle identity.

$\cos (2 \frac{π}{2}) + \sin (\frac{π}{2})$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Cancel the common factor.

$\cos (2 \frac{π}{2}) + \sin (\frac{π}{2})$

Step 3.1.2

Rewrite the expression.

$\cos (π) + \sin (\frac{π}{2})$

Step 3.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$- \cos (0) + \sin (\frac{π}{2})$

Step 3.3

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

$- 1 \cdot 1 + \sin (\frac{π}{2})$

Step 3.4

Multiply $- 1$ by $1$ .

$- 1 + \sin (\frac{π}{2})$

Step 3.5

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$- 1 + 1$

Step 4

Add $- 1$ and $1$ .

$0$