merimuradyany
Answered

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please help me

find
[tex] \sin(2x + \frac{5\pi}{4} ) [/tex]
if
[tex] \tan(x) = \frac{2}{3} [/tex]


​

Sagot :

Answer:

-17√2 /26 or -0.9247 to the nearest ten thousandth.

Step-by-step explanation:

The hypotenuse of the right triangle in which tan x = 2/3 is √(2^2 + 3^2)

= √13 so sin x = 2/√13 and cos x = 3/√13

sin2x = 2sinxcos

= 2* 2/√13 * 3/√13

= 12/13.

cos2x = cos^2x - sin^2x

= 9/13 - 4/13

= 5/13.

sin(2x + 5π/4)

= sin2x cos5π/4 + cos2x sin5π/4

= 12/13 * -1/√2 + 5/13 * -1/√2

= -12 / 13√2  - 5 / 13√2

= -17/13√2

= -17√2 /26.

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