Algebra Examples

2 cos (\frac{5 π}{3}) - sin (\frac{5 π}{2})

$2 \cos (\frac{5 π}{3}) - \sin (\frac{5 π}{2})$

Step 1

Simplify each term.

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Step 1.1

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

2 cos (\frac{π}{3}) - sin (\frac{5 π}{2})

$2 \cos (\frac{π}{3}) - \sin (\frac{5 π}{2})$

Step 1.2

The exact value of

cos (\frac{π}{3})

$\cos (\frac{π}{3})$ is

\frac{1}{2}

$\frac{1}{2}$ .

2 (\frac{1}{2}) - sin (\frac{5 π}{2})

$2 (\frac{1}{2}) - \sin (\frac{5 π}{2})$

Step 1.3

Cancel the common factor of

2

$2$ .

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Step 1.3.1

Cancel the common factor.

2 (\frac{1}{2}) - sin (\frac{5 π}{2})

$2 (\frac{1}{2}) - \sin (\frac{5 π}{2})$

Step 1.3.2

Rewrite the expression.

1 - sin (\frac{5 π}{2})

$1 - \sin (\frac{5 π}{2})$

1 - sin (\frac{5 π}{2})

$1 - \sin (\frac{5 π}{2})$

Step 1.4

Subtract full rotations of

2 π

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

0

$0$ and less than

2 π

$2 π$ .

1 - sin (\frac{π}{2})

$1 - \sin (\frac{π}{2})$

Step 1.5

The exact value of

sin (\frac{π}{2})

$\sin (\frac{π}{2})$ is

1

$1$ .

1 - 1 \cdot 1

$1 - 1 \cdot 1$

Step 1.6

Multiply

- 1

$- 1$ by

1

$1$ .

1 - 1

$1 - 1$

1 - 1

$1 - 1$

Step 2

Subtract

1

$1$ from

1

$1$ .

0

$0$