Trigonometry Examples

$2 \cos^{2} (20 - 1)$

Step 1

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

$2 (2 (\cos (20) \cdot \cos (1) + \sin (20) \cdot \sin (1)))$

Step 2

Simplify each term.

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Step 2.1

Evaluate $\cos (20)$ .

$2 (2 (0.93969262 \cdot \cos (1) + \sin (20) \cdot \sin (1)))$

Step 2.2

Evaluate $\cos (1)$ .

$2 (2 (0.93969262 \cdot 0.99984769 + \sin (20) \cdot \sin (1)))$

Step 2.3

Multiply $0.93969262$ by $0.99984769$ .

$2 (2 (0.9395495 + \sin (20) \cdot \sin (1)))$

Step 2.4

Evaluate $\sin (20)$ .

$2 (2 (0.9395495 + 0.34202014 \cdot \sin (1)))$

Step 2.5

Evaluate $\sin (1)$ .

$2 (2 (0.9395495 + 0.34202014 \cdot 0.0174524))$

Step 2.6

Multiply $0.34202014$ by $0.0174524$ .

$2 (2 (0.9395495 + 0.00596907))$

Step 3

Add $0.9395495$ and $0.00596907$ .

$2 (2 \cdot 0.94551857)$

Step 4

Multiply $2 (2 \cdot 0.94551857)$ .

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Step 4.1

Multiply $2$ by $0.94551857$ .

$2 \cdot 1.89103715$

Step 4.2

Multiply $2$ by $1.89103715$ .

$3.7820743$