Precalculus Examples

$5 π$

Step 1

Evaluate $\cos (5 π)$ .

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Step 1.1

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

$\cos (π)$

Step 1.2

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.

$- \cos (0)$

Step 1.3

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

$- 1 \cdot 1$

Step 1.4

Multiply $- 1$ by $1$ .

$- 1$

Step 2

Evaluate $\sin (5 π)$ .

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Step 2.1

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

$\sin (π)$

Step 2.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\sin (0)$

Step 2.3

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

$0$

Step 3

Set up the coordinates $(\cos (θ), \sin (θ))$ .

$(- 1, 0)$