Question

Please help me! Trying to raise my grade in PreCalc, right now we're working on trig functions. :/


A) What angle in the same quadrant as 30 degrees has the same cos value as cos 30 degrees?

B) What angle in a different quadrant as 30 degrees has the same cos value as cos 30 degrees?

C) What angle has a cos value that is the opposite of cos 30 degrees (-cos 30 degrees)?

Answer 1

@pooja195

Answer 2

This will give a major help, dear! :)

http://www.intmath.com/blog/mathematics/how-do-you-find-exact-values-for-the-sine-of-all-angles-6212

Answer 3

@Angel.Candy Thanks! Could you help me understand what the question is asking?

Answer 4

@Angel.Candy Thanks! Could you help me understand what the question is asking?

Answer 5

I believe its A : )

Answer 6

Haha, well, those aren't answer choices @Justin234

Answer 7

So here we have the unit circle

Answer 8

Part A) What angle in the same quadrant as 30 degrees has the same cos value as cos 30 degrees?

So first, which quadrant is 30 degrees in?

Answer 9

Top right, not sure which number that is though.

Answer 10

Oh that's fine, i mean in general it's:



But no big deal, as long as you know where it is

Answer 11

Awesome

Answer 12

Okay but good....so in that top right quadrant, between angles 0 and 90...what angle \(\large \theta\) would make \(\large cos(\theta) = cos(30)\)?


*If any....*

Answer 13

Well cos(30)=.154...

Answer 14

mmhmm...so what angle OTHER than 30, between 0 and 90, would equal that SAME result

*don't over think it :)

Answer 15

None?

Answer 16

Exactly! In that quadrant that holds 30 degrees, there are NO other angles that will give the same result!

So if we HAD to put an answer to this part...it would either be 30...or no other angles than 30

Answer 17

Awesome!

Answer 18

Mind helping me out with B & C? :)

Answer 19

No problem :)

So part B) What angle in a different quadrant as 30 degrees has the same cos value as cos 30 degrees?

So now ANY quadrant is game

Answer 20

So visually:



Now what other possible angles would replicate that cos(30) result?

Answer 21

Hint* Think about what quadrants cosine is positive or negative

Answer 22

The third quadrant?

Answer 23

Not quite...focus on that hint i put above *And now the added hint*

Answer 24

Ohhhh I see. So the fourth?

Answer 25

Exactly, since we know \(\large cos(30) = \frac{\sqrt{3}}{2}\) which is a positive number...we know that any other POSSIBLE angles would have to make cosine positive as well!

So that leaves angles in quadrant 1...or quadrant 4

So NOW what angle in quadrant 4 would give us the same result as cos(30)?

Answer 26

Hint* it would be just like reflecting it over the axis right?