WGW the zero point of the function FX = SiNx + acosx is 3 / 4 π 1. Find the value of real number A. 2. Let GX= WGW knows that a zero point of the function FX = SiNx + acosx is 3 / 4 π 1. Find the value of real number A. 2. Let GX = [FX] square - 2Sin square x, find the monotone increasing interval of GX

WGW the zero point of the function FX = SiNx + acosx is 3 / 4 π 1. Find the value of real number A. 2. Let GX= WGW knows that a zero point of the function FX = SiNx + acosx is 3 / 4 π 1. Find the value of real number A. 2. Let GX = [FX] square - 2Sin square x, find the monotone increasing interval of GX

Let GX = [FX] square - 2Sin square x, find the monotone increasing interval of GX (1) analytic: ∵ a zero of function FX = SiNx + acosx is 3 / 4 π, let sin φ = A / √ (1 + A ^ 2) f (x) = SiNx + acosx = √ (1 + A ^ 2) sin (x +...)

Given the function f (x) = SiNx + acosx, the image passes through the point (- π, 0)
1. Find the value of real number a
2. Let g (x) = [f (x)] ² - 2, find the minimum positive period and monotone increasing interval of image g (x)

A:
F (x) = SiNx + acosx passing through point (- π / 3,0)
Substitute:
f(-π/3)=sin(-π/3)+acos(-π/3)=0
So: √ 3 / 2 + A / 2 = 0
The solution is: a = √ 3
f(x)=sinx+√3cosx
=2*[(1/2)sinx+(√3/2)cosx]
=2sin(x+π/3)
g(x)=f²(x)-2
=4sin²(x+π/3)-2
=2*[1-cos(2x+2π/3)]-2
=-2cos(2x+2π/3)
G (x) minimum positive period T = 2 π / 2 = π
The monotone increasing interval satisfies:
2kπ

Given that the image of function f (x) = SiNx + acosx passes through the point (- π 3,0). (1) find the value of real number a; (2) find the minimum positive period and monotone increasing interval of function f (x)

When the image of F (x) = SiNx + acosx passes through the point (- π 3, 0), f (- π 3) = sin (− π 3) + ACOS (- π 3) = - 32 + a × 12 = 0, the solution is a = 3. (2) from (1) we know that f (x) = SiNx + 3cosx = 2Sin (x + π 3), the minimum positive period of F (x) t = 2 π 1 = 2 π, from 2K π