[Precalc] Trig Identities and Equations

[prefix]

Hello everyone

My book doesn't explain these very well, nor does it provide very many examples on how to solve the equations they list in the problems section. Anyway, I was wondering if anyone could help me with these two problems :

[Objective: Find all solutions to the given equation in the interval [0, 2pi). Give exact answers where possible.]

[#1] 4 cos x = cos x + 1
[#2] sin x cos x = 0

Thank you in advance.

 

[Mrspi]

Hello everyone

My book doesn't explain these very well, nor does it provide very many examples on how to solve the equations they list in the problems section. Anyway, I was wondering if anyone could help me with these two problems :

[Objective: Find all solutions to the given equation in the interval [0, 2pi). Give exact answers where possible.]

[#1] 4 cos x = cos x + 1
[#2] sin x cos x = 0

Thank you in advance.

[#1]
4 cos x = cos x + 1
Subtract cos x from both sides:
3 cos x = 1
Divide both sides by 3:
cos x = 1/3

Where in the interval [0, 2pi] does cos x = 1/3? Hint: there will be one solution in quadrant I, and one in quadrant IV.

[#2]
sin x cos x = 0
If the product of two factors is equal to 0, then at least one of the factors is equal to 0. So,

sin x = 0 or cos x = 0
Your knowledge of the unit circle should help you to identify the angles in [0, 2pi] for which sin x = 0, and for which cos x = 0.

I hope this helps you.

 

[prefix]

Hello everyone

My book doesn't explain these very well, nor does it provide very many examples on how to solve the equations they list in the problems section. Anyway, I was wondering if anyone could help me with these two problems :

[Objective: Find all solutions to the given equation in the interval [0, 2pi). Give exact answers where possible.]

[#1] 4 cos x = cos x + 1
[#2] sin x cos x = 0

Thank you in advance.

[#1]
4 cos x = cos x + 1
Subtract cos x from both sides:
3 cos x = 1
Divide both sides by 3:
cos x = 1/3

Where in the interval [0, 2pi] does cos x = 1/3? Hint: there will be one solution in quadrant I, and one in quadrant IV.

[#2]
sin x cos x = 0
If the product of two factors is equal to 0, then at least one of the factors is equal to 0. So,

sin x = 0 or cos x = 0
Your knowledge of the unit circle should help you to identify the angles in [0, 2pi] for which sin x = 0, and for which cos x = 0.

I hope this helps you.

Thank you, it does help.