Precalc question

Question

a) If y=sin(x) on the domain -π/2 ≤ x ≤ π/2, what is the domain D and range R of y=2sin(3x-1)+3? How many solutions does the equation 4=2sin(3x-1)+3 have on the domain D and what are they?

b) If y=cos(x) on the domain 0 ≤ x ≤ π, what is the domain D and range R of y=4cos(2x+1)-3? How many solutions does the equation -1=cos(2x+1)-3 have on the domain D and what are they?

c) If y=tan(x) on the domain -π/2 ≤ x ≤ π/2, what is the domain D and range R of y=2tan(-x+5)? How many solutions the equation have on 100=2tan(-x+5) the domain D and what are they?

Answer 1

Flora:

a)

4=2*sin(3x-1)+3. means. 2*sin(3x-1) = 1 or sin(3x-1) = 1/2. or 3x-1 = pi/6 so x=(1/3)*(pi/6 + 1)

b)

-1=4*cos(2x+1) -3. means. 2 = 4*cos(2x+1). or cos(2x+1) = 1/2. 2x+1 = pi/3 so x=(1/2)*(pi/3-1)

This is the general way to solve these kind of equations. I'll let you figure out the rest. Let me know if you need help