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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