Precalculus Examples

$- \frac{5 π}{2}$

Step 1

Evaluate $\cos (- \frac{5 π}{2})$ .

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Step 1.1

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

$\cos (\frac{3 π}{2})$

Step 1.2

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

$\cos (\frac{π}{2})$

Step 1.3

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$0$

Step 2

Evaluate $\sin (- \frac{5 π}{2})$ .

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Step 2.1

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

$\sin (\frac{3 π}{2})$

Step 2.2

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

$- \sin (\frac{π}{2})$

Step 2.3

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

$- 1 \cdot 1$

Step 2.4

Multiply $- 1$ by $1$ .

$- 1$

Step 3

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

$(0, - 1)$