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