Question

No idea where to start here: "Express the following in terms of sin A, cos A or tan A where 0 degrees is less than or equal to A and A is less than or equal to 90 degrees - tan 120.5 degrees."

Answer 1

Sorry I couldn't figure out to input an equation in the ask a question box

Answer 2

Bit of a wordy question there indeed! So \(0 \le A \le 90\). Look at the unit circle, and you'll see that you have to look at the first quandrant of a circle.

Answer 3

Yeah I know I have to use the circle, that's what we were learning about today. But what exactly do I do with it? What's the question asking?

Answer 4

The number given is \(120.5^{o}\), which is in the second quadrant. That means your first step is to find the reference angle. Do you know how to do that bit?

Answer 5

Hmm, is the reference angle the angle touching the middle of the circle?

Answer 6

If you draw a line at \(120.5^{o}\), it makes another angle to the horizontal axis (x-axis). That is the angle you have to find.

Answer 7

Isn't that just 180-120.5? 59.5?

Answer 8

It is!

Answer 9

Cool, but that's not the answer they're looking for is it? They want it expressed in terms or sin A cos A or tan A

Answer 10

When you have "- \(tan(120.5)\) above, does the - mean negative, or is it a hyphen to separate the two parts of the question?

Answer 11

We've found A so far, so we just have to decide whether to use sin, cos, or tan now.

Answer 12

It's a separator

Answer 13

Alright then. In the second quadrant, tan will be negative. By which I mean that \[tan(120.5) = -tan(59.5)\]

Answer 14

We can also express \(tanA\) as \[\frac{sinA}{cosA}\]

Answer 15

\[-tanA = \frac{-sinA}{-cosA}\]

Answer 16

Sorry, ignore one of those negative signs

Answer 17

Yeah, so how would you express the answer in the way the question says?

Answer 18

You could do it in two ways.\[tan(120.5)=-tan(59.5)\] or\[tan(120.5)=-\frac{sin(59.5)}{cos(59.5)}\]

Answer 19

Sweet, thanks. That's way easier than I thought. So just to make sure I've got it, I'll try and solve another example from the text book.

\[\cos(135) = -\cos(25)\]

Right? Or should I have not used cos?

Answer 20

That's right, except that 180-135 = 45, not 25 :P

Answer 21

Haha sorry about that. And \[-\sin (45) \] or

\[tan(45)\] would still be right?

Answer 22

Wait other way round. Switch the negative to the tan one

Answer 23

You have to consider the relationship \[tanA=\frac{sinA}{cosA}\] If you want to get cos in terms of sin and tan, you have to rearrange the equation to get cos on its own. What would that look like?

Answer 24

\[\sin(135) = cosA\] ?

Answer 25

Never mind I think I've got it. Thanks for the help :)