Answer: 0 < w ≤ 3/2
Sinx increasing interval (2kπ-π/2, 2kπ+π/2)
Sinwx increasing interval 2kπ-π/2
Interval contains 0
So it should be -π/2.
w & gt0
-π/2w & lt； x & ltπ/2w
(-π/3, π/4) is a subinterval.
So-π/2w
1/2w >= 1/3
w & lt=3/2
π/4 & lt； =π/2w
w & lt=2
0 & ltw & lt=3/2
Answer: 0 < w ≤ 3/2
2. Sin (π/2+a)+COS (π/2-a) =1/5a ∑ (0, π) to find tana?
cos(a)+sin(a)= 1/5
Both sides are squares,
1+2sinacosa= 1/25，
sin2a=-24/25，
Cos2a = (1-sin 2 (2a)) 0.5 = July 25th.
cosa= [( 1 cos(2a))/2]^0.5
cosa= 4/5，cosa= 3/5
sina= 3/5sin= 4/5
a∈(0，π)
Sina = 3/5 Sina =4/5
cosa+sina= 1/5
cosa=-3/5sina=4/5
tana=cosa/sina
Answer: -4/3
3. What is the minimum positive period and maximum value of the function y=sin(2x+π/6)-cos(2x+π/3)?
y=sin(2x+π/6)-cos(2x+π/3)
=sin2x*(3^0.5/2)+cos2x*( 1/2)-cos2x*( 1/2)+sin2x*(3^0.5/2)
=3^0.5sin(2x)
Minimum positive period T=2π/2=π
The maximum value is √3
Answer: π, 1 (What should I do with this function? )
4,5 π < A < 6 π, cosA/2=a, looking for Sina /4?
sin(a/2)=(( 1-cos(a/2)/2)^0.5
= (( 1-a)/2)^0.5
5π