Trigonometry Examples

- \frac{3 π}{4}

$- \frac{3 π}{4}$

Step 1

Take the cosine of

- \frac{3 π}{4}

$- \frac{3 π}{4}$ .

\cos (- \frac{3 π}{4})

$\cos (- \frac{3 π}{4})$

Step 2

Add full rotations of

2 π

$2 π$ until the angle is greater than or equal to

0

$0$ and less than

2 π

$2 π$ .

\cos (\frac{5 π}{4})

$\cos (\frac{5 π}{4})$

Step 3

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})

$- \cos (\frac{π}{4})$

Step 4

The exact value of

\cos (\frac{π}{4})

$\cos (\frac{π}{4})$ is

\frac{\sqrt{2}}{2}

$\frac{\sqrt{2}}{2}$ .

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

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

Decimal Form:

- 0.70710678 \dots

$- 0.70710678 \dots$

- \frac{3 π}{4}

$- \frac{3 π}{4}$

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