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Trig Functions help

Hey,

My maths teacher has told us to try and learn this over Easter, but I don't really understand it, she told us to go through these questions:

Screenshot from 2013-04-11 18:23:08.png

But in 10.5, I don't understand how you can get an equation with only one trigonometrical function, so how do they get rid of sin?

What is this called, are there any YouTube video tutorials on it?

Apart from that, I think I understand everything else.

Thanks!

Reply 1

aznkid66

sine and cosine can be substituted with a form of each other via the Pythagorean Identity (a trig identity):

\sin^2 x + cos^2 x = 1

In other words:

\sin x = \pm \sqrt{1 - cos^2 x}

\cos x = \pm \sqrt{1 - sin^2 x}

(edited 11 years ago)

Reply 2

TenOfThem

Original post by LewisL

But in 10.5, I don't understand how you can get an equation with only one trigonometrical function, so how do they get rid of sin?

They used the fact that

\sin ^2 A + \cos ^2 A = 1

Reply 3

.JJ

Sin^2theta + cos^2theta = 1
Rearrange that to get what you need, you'll be doing this alot.
In this case, you make the equation equal to sin^2theta by putting cos on the other side.

Reply 4

krisshP

Use Examsolutions for trigonometry, it helps a lot.

Reply 5

GhostIy

Brilliant! Thanks everyone, I understand that now :smile:

One more thing though, at the end when it says cos(theta) = 1/2 therefore (theta) = 60, how do I know to use inverse cos to get 60?

I don't really know when to use inverse for anything, I tried using cos at first for this until I realised the answer must be inverse as I was way out!

Reply 6

TenOfThem

Original post by LewisL

Brilliant! Thanks everyone, I understand that now :smile:

Are you serious?

You are doing A Level Maths and you do not know how to solve

\cos \theta = \dfrac{1}{2}

If you know what the cos is ... you have to find the angle ... we are talking some basic GCSE stuff here

Reply 7

GhostIy

Original post by TenOfThem

Are you serious?

You are doing A Level Maths and you do not know how to solve

\cos \theta = \dfrac{1}{2}

If you know what the cos is ... you have to find the angle ... we are talking some basic GCSE stuff here

Yeah, I only got a B for GCSE.

Haha, I remember now though, thank you!

Reply 8

GhostIy

Okay, my teacher wasn't in today, so I still haven't had a lesson on this.

Can someone help me with this question:

Screenshot from 2013-04-17 19:49:28.png

(4)

So for example, part (iii), my friend told me that you effectively rearrange it, so x is on it's own and then do inverse sin of the number, and I get -60, he then said you have to minus it from the nearest 90 degree's or something, he wasn't completely sure himself though, as he only learnt this from his tutor.

But anyway, the answers are 240 and 300. I'm guessing you minus 60 from 360, and then do it again or something, but I'm not sure why, can someone explain it to me please :frown: