Precalculus Examples

$2 \cos^{2} (- \frac{3 π}{8}) - 1$

Step 1

Apply the cosine double-angle identity.

$\cos (2 (- \frac{3 π}{8}))$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Move the leading negative in $- \frac{3 π}{8}$ into the numerator.

$\cos (2 \frac{- 3 π}{8})$

Step 2.2

Factor $2$ out of $8$ .

$\cos (2 \frac{- 3 π}{2 (4)})$

Step 2.3

Cancel the common factor.

$\cos (2 \frac{- 3 π}{2 \cdot 4})$

Step 2.4

Rewrite the expression.

$\cos (\frac{- 3 π}{4})$

Step 3

Move the negative in front of the fraction.

$\cos (- \frac{3 π}{4})$

Step 4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\cos (\frac{5 π}{4})$

Step 5

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 third quadrant.

$- \cos (\frac{π}{4})$

Step 6

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{2}}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{2}$

Decimal Form:

$- 0.70710678 \dots$