Question

What values for θ(0<θ<2pi) satisfy the equation 4 cos θ+1=2cosθ?

Answer 1

You just need to simplify the expression.

Answer 2

how?

Answer 3

Subtract 2cos θ from both sides.. That'll give you 2cos θ + 1 = 0

Answer 4

Simplifying it further.. 2cos θ=-1 ==> cos θ=-1/2

Answer 5

Now, at what θ is cos θ=-1/2 ? That should be your answer.

Answer 6

pi/3, 6pi/3?

Answer 7

umm nah.. cos pi/3=+1/2 and cos 6pi/3= cos 2pi=0

In which quad is cos theta negative?

Answer 8

...i dont really know, like at all haha

Answer 9

You need to learn one simple line for that..
Add Sugar To Coffee.

Add- A- All, which means all( cos, sin, tan) are +ve in the 1st quad.
Sugar - S- sin, which means sin is +ve in 2nd quad..
To - T - Tan, which means tan is +ve in 3rd quad.
Coffee- C - Cos, which means cos is +ve in 3rd quad.

So as you can see, cos is -ve in 2nd and 3rd quads. But as the question asks for x to be less than 2pi, we can narrow down on the 2nd quad..

Answer 10

Oh sorry. i just kinda messed up 2pi and pi.. so we have narrowed down on the 2nd and 3rd quads..

Answer 11

Following me?

Answer 12

Sort of :/ If you could break down the steps with the math i think id follow a bit better

Answer 13

We are almost done. You still need to remember in which quads cos is negative as we have a negative value.



Ok so.

Also you know cos pi/3 = +1/2

Our major aim is to take pi/3 to the second and third quads to make it give us a negative output.
Note you can only deal with pi.. Add subtracting pi/2 will change the expression to sin.

So you just need to add pi to take it to the third quad..
which will give you pi/3+ pi = 4pi/3

Now how can you take it to the 2nd quad?
pi-x.. so pi-(pi/3)= 2pi/3

Answer 14

Well i just realised i didnt explain it like it has to be. You should wait for someone else to come and help you better. Tried my best though.