Trigonometry Examples

$\sin (33 ° + 42 °)$

Step 1

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

$\sin (33 °) \cos (42 °) + \cos (33 °) \sin (42 °)$

Step 2

Remove parentheses.

$\sin (33 °) \cos (42 °) + \cos (33 °) \sin (42 °)$

Step 3

Simplify each term.

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Step 3.1

Evaluate $\sin (33 °)$ .

$0.54463903 \cos (42 °) + \cos (33 °) \sin (42 °)$

Step 3.2

Evaluate $\cos (42 °)$ .

$0.54463903 \cdot 0.74314482 + \cos (33 °) \sin (42 °)$

Step 3.3

Multiply $0.54463903$ by $0.74314482$ .

$0.40474568 + \cos (33 °) \sin (42 °)$

Step 3.4

Evaluate $\cos (33 °)$ .

$0.40474568 + 0.83867056 \sin (42 °)$

Step 3.5

Evaluate $\sin (42 °)$ .

$0.40474568 + 0.83867056 \cdot 0.6691306$

Step 3.6

Multiply $0.83867056$ by $0.6691306$ .

$0.40474568 + 0.56118014$

Step 4

Add $0.40474568$ and $0.56118014$ .

$0.96592582$