You are Here: Home >< Maths

# C2 Trigonometric Equations

Announcements Posted on
Why bother with a post grad? Are they even worth it? Have your say! 26-10-2016
1. Hi, can anyone provide me with the steps to solve a trignometric equation as well as how find the other possible values within the given range? I've tried the CAST diagram but it just confuses me. Would really appreciate any feedback and am happy to try and help with any AS Maths topics? Thanks
2. you can do it on a calc
3. (Original post by The gains kinggg)
you can do it on a calc
Eventually yes but I need to know the steps to do so.
4. (Original post by AspieMagic)
Hi, can anyone provide me with the steps to solve a trignometric equation as well as how find the other possible values within the given range? I've tried the CAST diagram but it just confuses me. Would really appreciate any feedback and am happy to try and help with any AS Maths topics? Thanks
CAST Diagram is way easier. Here is a great video explaining it. https://youtu.be/XMXOglASh00

if you have something like sin3x=1/2. The three just means you take 3 revolutions. the values depend on the range (e.g positive or negative).
5. Give a question you're struggling with. I can help (;
It's all just being able to manipulate what trig identity to use.
(Original post by AspieMagic)
Hi, can anyone provide me with the steps to solve a trignometric equation as well as how find the other possible values within the given range? I've tried the CAST diagram but it just confuses me. Would really appreciate any feedback and am happy to try and help with any AS Maths topics? Thanks
6. Use ExamSolutions! Just type it into Google and find your exam board. There are exam questions which you could watch the guy do at the bottom of trig section "Exam Questions". There is video solution where he goes through it. He uses CAST but it really does make sense after watching his videos. - (The exam questions are edexcel but don't differ hugely between boards)
7. (Original post by Paranoid_Glitch)
CAST Diagram is way easier. Here is a great video explaining it. https://youtu.be/XMXOglASh00

if you have something like sin3x=1/2. The three just means you take 3 revolutions. the values depend on the range (e.g positive or negative).
Okay thanks, I'll try that.
8. (Original post by Yusufff)
Use ExamSolutions! Just type it into Google and find your exam board. There are exam questions which you could watch the guy do at the bottom of trig section "Exam Questions". There is video solution where he goes through it. He uses CAST but it really does make sense after watching his videos. - (The exam questions are edexcel but don't differ hugely between boards)
Okay great - am on Edexcel so that's perfect.
9. (Original post by ovo_zverit)
Give a question you're struggling with. I can help (;
It's all just being able to manipulate what trig identity to use.
None in particular, it's what to do with the initial x value you find?:3
10. I second the Examsolutions suggestion, but if you really don't like/don't want to use CAST, you could draw the graph to visually represent any solutions (make sure you draw it correctly, given any transformations too otherwise it might mislead you to incorrect solutions).
11. Sin > 180 - First Answer, 180 + first answer, 360 + ( depending on range)
Cos > 360 - First Answer, 360 + a, 720 - A ( depending on range)
Tan > 180 + a, second answer + 180, and add on 180 until out of range

I think this is how... and for trig equations cos^2x= 1- sin^x , most of the time you need to rearange the formula and probably get a quadric, replace all cos with y or x than solve it, you'll probably get something like (2x-1) (x-3) sub back in cos/tan/sin than solve it

i think its right, correct me pls if am wrong
12. (Original post by Virolite)
I really hope you're not sitting c2 maths tomorrow, for your own sake
That's pretty unkind and do not think for a second that it's because I've been slacking off. I've worked so hard for this but there are a few concepts I sometimes need reminding of. I didn't ask you to make unsettling comments so if you can't or don't want to help then you should just keep your thoughts to yourself
Sin > 180 - First Answer, 180 + first answer, 360 + ( depending on range)
Cos > 360 - First Answer, 360 + a, 720 - A ( depending on range)
Tan > 180 + a, second answer + 180, and add on 180 until out of range

I think this is how... and for trig equations cos^2x= 1- sin^x , most of the time you need to rearange the formula and probably get a quadric, replace all cos with y or x than solve it, you'll probably get something like (2x-1) (x-3) sub back in cos/tan/sin than solve it

i think its right, correct me pls if am wrong
This is exactly what I meant, thank you ever so much!
14. (Original post by tripleseven)
I second the Examsolutions suggestion, but if you really don't like/don't want to use CAST, you could draw the graph to visually represent any solutions (make sure you draw it correctly, given any transformations too otherwise it might mislead you to incorrect solutions).
Thanks - will give the CAST diagram another shot.
15. (Original post by AspieMagic)
That's pretty unkind and do not think for a second that it's because I've been slacking off. I've worked so hard for this but there are a few concepts I sometimes need reminding of. I didn't ask you to make unsettling comments so if you can't or don't want to help then you should just keep your thoughts to yourself
nuff said.
16. can anyone help me with this?
i understand how to work out equations such as
sin(theta)=0.5, using a drawing of the graph, (I can't understand the CAST method) but when it's like
3sin(theta)=0.5 i don't understand what to do with the extra number (the 3).
any help?
thanks x
17. (Original post by louisedrake)
can anyone help me with this?
i understand how to work out equations such as
sin(theta)=0.5, using a drawing of the graph, (I can't understand the CAST method) but when it's like
3sin(theta)=0.5 i don't understand what to do with the extra number (the 3).
any help?
thanks x
Divide both sides by 3, so sin (theta) = 0.5/3 = 1/6, then it's just a normal equation sin (theta) = 1/6 which you solve the same way.
18. (Original post by louisedrake)
can anyone help me with this?
i understand how to work out equations such as
sin(theta)=0.5, using a drawing of the graph, (I can't understand the CAST method) but when it's like
3sin(theta)=0.5 i don't understand what to do with the extra number (the 3).
any help?
thanks x
Divide 0.5 by 3x
19. (Original post by AspieMagic)
This is exactly what I meant, thank you ever so much!
No probb
20. (Original post by AspieMagic)
Hi, can anyone provide me with the steps to solve a trignometric equation as well as how find the other possible values within the given range? I've tried the CAST diagram but it just confuses me. Would really appreciate any feedback and am happy to try and help with any AS Maths topics? Thanks
i think CAST is the fastest way to solve and easiest
Look at the diagram i attached i literally included everything u need to know cast.

the second angle u work out is always referenced from the HORIZONTAL line NOT VERTICAL

if you have a positive angle for sin or cos or tan

u look at the cast diagram and look for the corresponding function and work out the angle using horizontal line as reference point.

if you have a negative angle for sin or cos or tan

u look at the cast diagram and look for the 2 functions that are not "ALL" and the function u just worked out

Example for positive angle:
Sin(x)=0.5 for 0<x<360
x=30 degrees (this is your first solution that is inside the "ALL" quadrant, note your first positive angle for sin or cos or tan will ALWAYS be inside the "ALL" quadrant)

now we look at the corresponding function on the cast diagram which is S for sin
to work out that angle we do 180-30 = 150 degrees, so x = 30, 150.

Example for negative angle:
tan(x) = -1 for 0<x<360
x = -45 degrees (note -45 degrees cannot be inside the "ALL" quadrant because it is less than 0 degrees)

to work out the solutions you look at the functions that are NOT tan and NOT inside the "ALL" quadrant.
In this case we look for cos and sin.
ignore the minus sign for now on the -45 degrees (always ignore it when working out the solutions that are not negative), and work out cos and sin quadrant normally
for cos quadrant u do 360-45 = 315
for sin quadrant u do 180-45 = 135

so your solutions to tan(x)=-1 are x = 135, 315 degrees.

there are more to know but its long to explain 1 day before the exam lol
if you are not comfortable with cast stick to your way of working it out, this wil help people who are already a little bit experienced with cast
Attached Images

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: May 24, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

### University open days

Is it worth going? Find out here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read here first

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams