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IceJOKER [234]
3 years ago
13

If cosA = 3/5 and A ∈ (630,720), find sin2A

Mathematics
1 answer:
Sergio039 [100]3 years ago
5 0

Answer:

- \frac{24}{25}

Step-by-step explanation:

Given 630 < A > 720 then A is in the fourth quadrant where

cosA > 0 and sinA < 0

Given

cosA = \frac{3}{5} = \frac{adjacent}{hypotenuse}

Then the triangle is a 3- 4 - 5 with opposite side 4, thus

sinA = - \frac{opposite}{hypotenuse} = - \frac{4}{5}

Using the trigonometric identity

sin2A = 2sinAcosA

         = 2 × - \frac{4}{5} × \frac{3}{5}

         = \frac{2(-4)(3)}{5(5)} = - \frac{24}{25}

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