Algebra Examples

$\cos (90)$

Step 1

The angle $90$ is an angle where the values of the six trigonometric functions are known. Because this is the case, add $0$ to keep the value the same.

$\cos (90 + 0)$

Step 2

Use the sum formula for cosine to simplify the expression. The formula states that $\cos (A + B) = - (\cos (A) \cos (B) + \sin (A) \sin (B))$ .

$\cos (0) \cdot \cos (90) - \sin (0) \cdot \sin (90)$

Step 3

Remove parentheses.

$\cos (0) \cdot \cos (90) - \sin (0) \cdot \sin (90)$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

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

$1 \cdot \cos (90) - \sin (0) \cdot \sin (90)$

Step 4.2

Multiply $\cos (90)$ by $1$ .

$\cos (90) - \sin (0) \cdot \sin (90)$

Step 4.3

The exact value of $\cos (90)$ is $0$ .

$0 - \sin (0) \cdot \sin (90)$

Step 4.4

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

$0 - 0 \cdot \sin (90)$

Step 4.5

Multiply $- 1$ by $0$ .

$0 + 0 \cdot \sin (90)$

Step 4.6

The exact value of $\sin (90)$ is $1$ .

$0 + 0 \cdot 1$

Step 4.7

Multiply $0$ by $1$ .

$0 + 0$

Step 5

Add $0$ and $0$ .

$0$