Find the value range of the square of function y = (cosx) + sinxcosx

Find the value range of the square of function y = (cosx) + sinxcosx

Y = (cosx) ^ 2 + sinxcosx = (2 (cosx) ^ 2-1) / 2 + 1 / 2 + (1 / 2) sin2x = (1 / 2) cos2x + (1 / 2) sin2x + 1 / 2 = (1 / 2) sin (2x + pi / 4) + 1 / 2 (1 / 2) sin (2x + pi / 4) is a closed interval from - 1 / 2 to 1 / 2, then y is the closed interval of 0 to 1

The value range of the square of the function y = CO (x - π / 4) - cos (x + π / 4) is

y=cos²(x-π/4)²-cos(x+π/4)²
=cos(π/4-x)²-sin(π/4-x)²
=cos(π/2-2x)
=sin(2x)
The range is [- 1,1]

What are the minimum positive periods and ranges of the function y = 1 / 2-cos square x?

y=1/2-(cosx)^2=1/2-(1+cos2x)/2=cos2x/2
So t = 2 π / 2 = π
The range is [- 1 / 2,1 / 2]

Value domain of y = cos square x + cosxsinx

y=(1+cos2x)/2+1/2*sin2x
=1/2*(sin2x+cos2x)+1/2
=√2/2*sin(2x+π/4)+1/2
-1

Find the value range of the function y = cos + SiNx + cosxsinx

Let t = SiNx + cosx
be
t=√2sin(x+45°)∈[-√2,√2]
And sinxcosx
=[(sinx+cosx)^2-(sinx)^2-(cosx)^2]/2
=(t^2-1)/2
The original formula = t + (T ^ 2-1) / 2
=[(t+1)^2-2]/2
y∈[-1,(1+2√2)/2]

The value range of the function y = radical 3sinx + cos (- x) is

y=√3sinx+cos（-x）
=√3sinx+cosx
=2(sinx*√3/2+1/2*cosx)
=2sin(x+30º)
∵-1≤sin(x+30º)≤1
∴-2≤2sin(x+30º)≤2
The range is [- 2,2]

The value range of cos α - 1 under y = radical I'm a sophomore in high school. I can't understand it

Y = radical (COS α - 1)
There is no negative number under the radical, cos α - 1 ≥ 0, cos α ≥ 1
And: - 1 ≤ cos α ≤ 1
∴cosα=1
ν y = root (COS α - 1) = root 0 = 0
Range: [0]

The range of y = 7 / 4sinx cos ^ 2x RT

Y = 7sinx / 4-cos? X = 7sinx / 4-1 + sin? X = (sin? 2x + 7sinx / 4 + 49 / 64) - 49 / 64-1 = (SiNx + 7 / 8) Ω - 113 / 64, so it is appropriate that the minimum value of SiNx = - 1 is: - 7 / 2, and the maximum value is: 7 / 2 when SiNx = 1

Find the value range of the function y = cos ^ 2x-4sinx + 6

Using the same angle relation + substitution method
y=cos^2x-4sinx+6
=1-sin²x-4sinx+6
=-sin²x-4sinx+7
Let t = SiNx, then - 1 ≤ t ≤ 1
∴ y=-t²-4t+7
=-(t+2)²+11
It's a quadratic function of T with the opening downward and the axis of symmetry t = - 2
When t = - 1, y has a maximum value of 10
When t = 1, y has a minimum value of 2
The value range of the function y = cos ^ 2x-4sinx + 6 is [2,10]

Find the range of X ∈ [- π / 6, π / 6] of the function y = 6-4sinx cos ^ 2x

y∈[13/4,29/4]
Draw a picture and have a look at it