Answer:
-17β2 /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 β(2^2 + 3^2)
= β13 so sin x = 2/β13 and cos x = 3/β13
sin2x = 2sinxcos
= 2* 2/β13 * 3/β13
= 12/13.
cos2x = cos^2x - sin^2x
= 9/13 - 4/13
= 5/13.
sin(2x + 5Ο/4)
= sin2x cos5Ο/4 + cos2x sin5Ο/4
= 12/13 * -1/β2 + 5/13 * -1/β2
= -12 / 13β2 - 5 / 13β2
= -17/13β2
= -17β2 /26.
