Question

If sin alpha = 4/5 then find the value of sin 2 alpha.

Answer 1

Finding the value:

Step-by-step explanation:

$\ Given \ value: \\\\\sin \alpha \ = \frac{4}{5} \\\\\ Find: \\\\\sin 2 \alpha\\\\\ Solution: \\\\\sin \alpha \ = \frac{P}{H} = \frac{4}{5} \\\\\cos \alpha \ = \frac{B}{H} = ?\\\\ H^2\ = P^2+B^2 \\\\5^2=4^2+B^2\\\\25=16+B^2\\\\25-16\ = B^2\\\\9 =B^2\\\\B^2=3^2\\\\\ B \ = \ 3 \\\\\cos \alpha = \frac{B}{H}\ =\frac{3}{5}$

$\ formula: \\\\\sin 2\alpha = 2 \sin\alpha \cos \alpha\\\\\rightarrow \sin 2\alpha = 2 \times \frac{4}{5} \times \frac{3}{5} \\\\\rightarrow \sin 2\alpha = 2 \times \frac{12}{25}\\\\\rightarrow \sin 2\alpha = \frac{24}{25}$

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