Question

Little help, please. Does anyone know how the heck to do this?!
cosθ - tanθcosθ = 0 . . . I don't get it. O-o

Answer 1

You are given cosθ - tanθcosθ = 0 and asked to find theta, correct?

Answer 2

I believe so. P.S. Sorry to leave you hanging like that, I was AFK. o~o

Answer 3

Okay so notice that cosθ is common to both terms on the left side so we can factor it out to get

cosθ(1 - tanθ) = 0 right?

Answer 4

Sounds right.

Answer 5

Whenever you have two terms and a number or variable is common to both, you can use factoring for simplification purposes. In this case, we end up with the form

ab = 0, therefore we can apply zero product property which says if ab = 0, then
a = 0 or b = 0. Are you familiar with that?

Answer 6

Because 0 times any number equals 0. Correct?

Answer 7

Because, you know, if we let a = cosθ and b = 1 - tanθ, then by zero product property we can say

cosθ = 0 or
1 - tanθ = 0

Answer 8

Okay.

Answer 9

Okay, so do you believe you can solve for θ from here?

Answer 10

I enter it into my calculator I think. But I'm not sure how I would input that.

Answer 11

Well you can solve one equation at a time. Remember, we are trying to find θ. So if you solve cosθ = 0, then you can take the inverse cosine of both sides to get

\(θ = \cos^{-1}(0)\)

Answer 12

I had forgotten about the inverse.

Answer 13

How do you think we should handle 1 - tanθ = 0?

Answer 14

θ=tanθ ^-1 +1?

Answer 15

Well with 1 - tanθ = 0, what you want to do is first isolate tanθ to one side. Then isolate θ.

So
1 - tanθ = 0
1 = tanθ (after adding tanθ to both sides).

Get it?

Answer 16

So tanθ=1, so cos^-1=0. So we found the zero.

Answer 17

Once you use the zero product property, you will have two equations, which usually implies that there are two values to find for each equation.

You will find a value of theta for cosθ = 0 and a value of theta for 1 - tanθ = 0

Answer 18

We should expect both values to be different.

Answer 19

We don't just solve one equation and then assume that the value we get will be the same for the other. We must solve both equations and we must get two values of theta.

Answer 20

I don't understand the set of answers they have.

Answer 21

When solving problems, you should do one step at a time.

Answer 22

Don't jump to the back of the book until you have attempted to solve the problems first.

Answer 23

But nevertheless, from the answer choices, it means your calculator should be placed in radian mode.

Answer 24

Alrighty, I just don't get where (pi) comes into to play. But, I'll get there no doubt.

Answer 25

Ah cripes! My REAL graphing calculator is with my brother. Will a TI-30XA, suffice?

Answer 26

I abandoned anything other than TI-Nspire calcs long ago. I suggest that you get one.

Answer 27

That's a good idea.

Answer 28

I'll let you go. Thank you for your help, @Hero . Maybe I'll bump into you on another question.