Trig Questions

[shanem]

I have a couple problems I cannot figure out. If anyone could help me I would greatly appreciate it.

1. Solve 3sin(2x)=2cos(x) on [0,2pi) algebraically (answers in terms of pi)


2. Determine whether equation is conditional or identity
sin(A +B) + sin(A-B)= 2sinAcosB

3. Find all solutions to the equations cos^2(x) + sin(x) + 1= 0 in the interval [0,2pi) algebraically (answers in terms of pi)

 

[Deleted member 4993]

Please show your work so that we can help you properly.

I have a couple problems I cannot figure out. If anyone could help me I would greatly appreciate it.

1. Solve 3sin(2x)=2cos(x) on [0,2pi) algebraically (answers in terms of pi)

3*sin(2x) = 2*cos(x)

6*sin(x) * cos(x) = 2*cos(x)

6*sin(x) * cos(x) - 2*cos(x) = 0

2*cos(x) * [3sin(x) -1] = 0

Now finish it....


2. Determine whether equation is conditional or identity
sin(A +B) + sin(A-B)= 2sinAcosB

Expand sin(A+B) and sin(A-B) and resolve

3. Find all solutions to the equations cos^2(x) + sin(x) + 1= 0 in the interval [0,2pi) algebraically (answers in terms of pi)

cos^2(x) + sin(x) + 1= 0

1 - sin^2(x) + sin(x) + 1= 0

sin^2(x) - sin(x) - 2 = 0

Above is a quadratic equation - solve it...