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Ask the math master to do a function problem
( 1)f(π)=2sin(π/3+φ)=2,∴sin(π/3+φ)= 1

And 0

∴π/3+φ=π/2,∴φ=π/6

(2)f(x)=2sin(x/3+π/6)

Then f (3a+π) = 2sin (a+π/3+π/6) = 2sin (a+π/2) = 2cosa =10/13.

∴cosa=5/ 13, and a∈[-π/2, o], ∴ Sina < 0, then Sina =- 12/ 13.

∴f(3a-5π/4)=2sin(a-5π/ 12+π/6)

=2sin(a-π/4)

=2 (Sina *√2/2-cosa*√2/2)

=√2* (Sina -cosa)

=√2*(- 12/ 13-5/ 13)

=- 17√2/ 13

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