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System Message

[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Guest (Customer)

[00:00:00] Can you explain trigonometric functions?

Aaron S (Tutor)

[00:00:06] Welcome to Tutor.com !
Let's get started.

Guest (Customer)

[00:00:12] Sounds good

Aaron S (Tutor)

[00:00:37] Do you have a particular problem you'd like me to work out?
Or would you like me to just explain the basic concept of trigonometric functions?

Guest (Customer)

[00:01:04] Explain the basic concept of
the powers used in trig

[00:01:15] like sin theta ^2

[00:01:16] then

Aaron S (Tutor)

[00:01:27] Okay, so trigonometric identities?

Guest (Customer)

[00:01:29] (sin theta)^2

Aaron S (Tutor)

[00:01:52] Okay, well that's more about algebra than trigonometry.
Let me use the board to explain.

Guest (Customer)

[00:01:56] ok

[00:02:36] what about sin^2 theta

[00:02:38] too

[00:02:41]

[00:02:54] I see okay

Aaron S (Tutor)

[00:03:02] That's just another way of writing it.

[00:03:14] But with sin theta^2, you would square the theta before taking the sine.

[00:03:35] In contrast, with (sin theta)^2, you take the sine of theta, then after that you square your solution.

[00:03:51] Basically, it's just a matter of order of operations.

Guest (Customer)

[00:03:55] I see

[00:04:05] That makes sense

Aaron S (Tutor)

[00:04:23] And if try plugging a number in for theta, you'll see that you get a different answer if you square before taking the sine compared to squaring after taking the sine.

Guest (Customer)

[00:05:12] Okay I see.

[00:05:15]

Aaron S (Tutor)

[00:05:26] So do you understand everything now?

Guest (Customer)

[00:05:25] That was a lot easier than I
thought.

[00:05:28] Yes

[00:05:30]

Aaron S (Tutor)

[00:05:38] Great!
Do you have any other questions that I can help out with?

Guest (Customer)

[00:05:53] Yes!

[00:05:59] sin ^3 (-60)

Aaron S (Tutor)

[00:06:09] You just want to solve that expression?

Guest (Customer)

[00:06:19] Yes

Aaron S (Tutor)

[00:06:55] As I explained earlier, if you have sin^3, you actually do the exponent after taking the sine of that angle.

[00:07:09] So how about you try solving this yourself, and I'll let you know how it looks as you go.

Guest (Customer)

[00:07:25] Sounds great!

[00:07:31] so sin of -60 is

[00:07:44] -0.866

Aaron S (Tutor)

[00:07:57] Right!
You can also say that it is sqrt(3)/2.

[00:08:14] That might be better for our purposes.
That way, you'll see the exact value rather than a rounded decimal.

[00:08:37] Sorry, I meant -sqrt(3)/2.

Guest (Customer)

[00:08:39] We get that from the unit
circle right?

Aaron S (Tutor)

[00:08:44] Right.

Guest (Customer)

[00:08:45] Okay!

Aaron S (Tutor)

[00:09:03] Now all you need to do is apply the exponent.

Guest (Customer)

[00:09:04] Sqrt of 3 ^3

Aaron S (Tutor)

[00:09:18] Do you know how to simplify that?

Guest (Customer)

[00:09:34] Without getting a decimal...
no.

[00:09:36]

[00:09:42] oh wait

[00:10:06] Can we just get rid of the sqrt
because we have power of
three which has ^2 within it?

Aaron S (Tutor)

[00:10:32] Well that's close.
I think we should start on a different part though.

[00:10:41] To start out, is our answer going to be positive or negative?

Guest (Customer)

[00:10:46] Negative

Aaron S (Tutor)

[00:11:01] Right.
Then we can distribute the exponent to the numerator and denominator...

[00:11:21] What does the denominator become when you evaluate 2^3?

Guest (Customer)

[00:11:36] 8

Aaron S (Tutor)

[00:11:40] Good!

[00:12:06] Now I'm going to separate the sqrt(3) terms out and give you a hint for how to simplify.

Guest (Customer)

[00:12:11] Okay

[00:12:35] 9*sqrt3?

Aaron S (Tutor)

[00:12:54] Well that's close, let me take one more step for you though...

Guest (Customer)

[00:12:57] Okay

Aaron S (Tutor)

[00:13:12] It's actually the square root of 9.

Guest (Customer)

[00:13:15] okay

Aaron S (Tutor)

[00:13:27] And what is the square root of 9?

Guest (Customer)

[00:13:34] 3

[00:13:46] I see!

Aaron S (Tutor)

[00:13:49] And that's your solution!

[00:13:56] Do you see how we got that?

Guest (Customer)

[00:14:00] I do

[00:14:01] however

[00:14:15] I thought that a sqrt*sqrt
cancelled

[00:14:18] is that not true?

Aaron S (Tutor)

[00:14:36] It does, but when it cancels, you don't multiply the numbers.
You just leave it as 3.

[00:14:54] You were right to cancel it, but then you multiplied the 3's.

[00:15:12] And it wouldn't make sense to say that sqrt(3)*sqrt(3) is equal to the same thing as 3*3.

Guest (Customer)

[00:15:21] I see.

[00:15:29] I have another problem.

Aaron S (Tutor)

[00:15:35] Okay, let's see it

Guest (Customer)

[00:15:37] Alright!

[00:15:45] csc^2 - tan 45 deg

Aaron S (Tutor)

[00:16:12] Did you forget something there?
It just says csc^2, it doesn't say what you're taking the cosecant of.

Guest (Customer)

[00:16:20] oh sorry

[00:16:23] 405

[00:16:26] degrees

Aaron S (Tutor)

[00:16:51] Okay, great!
Do you have an idea how to begin with this problem?

Guest (Customer)

[00:17:17] Yes

[00:17:31] So csc^2(405) is the same as

[00:17:50] csc(405)

[00:17:52] ^2

Aaron S (Tutor)

[00:18:14] Good!

Guest (Customer)

[00:18:19] csc is the recp. of sin

[00:18:25] and will be positive

Aaron S (Tutor)

[00:19:02] Alright, now you can actually change that 405 angle to something that looks a little more familiar.

[00:19:25] Think back to the unit circle.
Wouldn't 405 go completely around the circle?

[00:19:33] And then a little further than that?

Guest (Customer)

[00:19:36] Right

Aaron S (Tutor)

[00:19:55] So wouldn't the 405 angle be the same thing as that angle minus 360?

Guest (Customer)

[00:20:23] or 45 degrees?

Aaron S (Tutor)

[00:20:28] Right!

Guest (Customer)

[00:20:52] sin 45 is sqrt2/2 right?

Aaron S (Tutor)

[00:21:02] Right.

Guest (Customer)

[00:21:07] HOORAY!

[00:21:17] Now

[00:21:37] I am going to need a hint

[00:21:41] no

Aaron S (Tutor)

[00:21:58] You've got this

Guest (Customer)

[00:21:57] Is it just 1/2/2?

[00:22:09] That doesn't make sense

Aaron S (Tutor)

[00:22:20] Well let's solve what's inside the parenthesis first.

Guest (Customer)

[00:22:25] Okay

Aaron S (Tutor)

[00:22:33] Can you simplify that to one fraction instead of a fraction within a fraction?

Guest (Customer)

[00:22:50] Sure

[00:22:59] Would it become 2/sqrt2

Aaron S (Tutor)

[00:23:06] Good!

[00:23:39] Now you can distribute that exponent to the numerator and denominator.

Guest (Customer)

[00:24:10] 2*2/sqrt2*sqrt2=4/sqrt4

Aaron S (Tutor)

[00:24:34] Looks good!

[00:24:38] What can you do next?

Guest (Customer)

[00:24:44] I have to face tan 45

Aaron S (Tutor)

[00:24:54] Well not yet...

Guest (Customer)

[00:24:57] okay good.

Aaron S (Tutor)

[00:25:00] Can't you simplify sqrt(4)?

Guest (Customer)

[00:25:05] yes!

[00:25:12] sqrt of 4 is 2

[00:25:28] 2- tan 45

Aaron S (Tutor)

[00:25:43] Okay, now we have to face tan(45).

[00:25:52] What do you think it would be?

Guest (Customer)

[00:26:25] Tan is sin/cos right?

Aaron S (Tutor)

[00:26:31] Right.

[00:26:58] And you already know sin(45) and cos(45).

Guest (Customer)

[00:27:07] sin 45 is sqrt2/2

[00:27:15] same for cos

[00:27:23] which is 1!

[00:27:31] and then 1 again

Aaron S (Tutor)

[00:27:40] That's correct, great job!!

[00:27:55] It was just a little tedious, but nothing you can't handle.

Guest (Customer)

[00:27:59] Agreed!

[00:28:04] Just tedious

Aaron S (Tutor)

[00:28:09] So do you have any questions about how we solved that one?

Guest (Customer)

[00:28:14] I don't

[00:28:19] Thank you for your help!!!!!

Aaron S (Tutor)

[00:28:25] Okay, well I'm glad I've been able to help!

[00:28:30] Thanks for using Tutor.com.Â Please fill out the survey as you leave so we can learn how we can better help you in the future!Â

Guest (Customer)

[00:28:40] I will!
Have a great night!

Aaron S (Tutor)

[00:28:48] Thanks!
You too!

Guest (Customer)

[00:28:50] Bye!

Aaron S (Tutor)

[00:28:54] Goodbye