Expand Using Sum/Difference Formulas cos(90)

$\cos (90)$

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.

$\cos (90 + 0)$

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

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

Remove parentheses.

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

Simplify each term.

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

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

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

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

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

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

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

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

Multiply $- 1$ by $0$ .

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

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

$0 + 0 \cdot 1$

Multiply $0$ by $1$ .

$0 + 0$

Add $0$ and $0$ .

$0$

Expand Using Sum/Difference Formulas cos(90)

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