Turn on thread page Beta
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by Notnek)
    E.g.

    \sin y = x

    becomes

    y = \arcsin x

    You can do a similar thing here.
    \cos y = \sin\left(\frac{\pi}{2}-y\right)

    \sin y = \cos\left(\frac{\pi}{2}-y\right)

    i that right?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by Notnek)
    E.g.

    \sin y = x

    becomes

    y = \arcsin x

    You can do a similar thing here.
    i don't get how you replaced to x inside the identity with a y?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Maths&physics)
    i don't get how you replaced to x inside the identity with a y?
    Can you please show me which line of working you don’t understand?
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by Notnek)
    Can you please show me which line of working you don’t understand?
    \Rightarrow \sin\left(\frac{\pi}{2}-y\right) = x

    where did the y come from inside the identity?
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (Original post by Maths&physics)
    \Rightarrow \sin\left(\frac{\pi}{2}-y\right) = x

    where did the y come from inside the identity?
    The identity is

    \cos A \equiv \sin \left(\frac{\pi}{2}-A\right)

    I'm using A here because I think the x/y may be confusing. This is an identity so you can replace A with anything. Back to the working:

    y=arccos(x)

    \Rightarrow \cos(y) = x (*)

    I'm labeling the line above with a (*) to refer to it later.


    Then using the identity above, you can replace A with y to give

    \cos y = \sin \left(\frac{\pi}{2}-y\right)

    So then the line of working (*) becomes

    \sin \left(\frac{\pi}{2}-y\right) = x

    Then you can move the sin to the other side:

    \frac{\pi}{2}-y = \arcsin x
    • Thread Starter
    Offline

    12
    ReputationRep:
    (Original post by Notnek)
    The identity is

    \cos A \equiv \sin \left(\frac{\pi}{2}-A\right)

    I'm using A here because I think the x/y may be confusing. This is an identity so you can replace A with anything. Back to the working:

    y=arccos(x)

    \Rightarrow \cos(y) = x (*)

    I'm labeling the line above with a (*) to refer to it later.


    Then using the identity above, you can replace A with y to give

    \cos y = \sin \left(\frac{\pi}{2}-y\right)

    So then the line of working (*) becomes

    \sin \left(\frac{\pi}{2}-y\right) = x

    Then you can move the sin to the other side:

    \frac{\pi}{2}-y = \arcsin x
    thank you.

    cos(y) doesn't = x in the cos graph, but yes, in this case it does, do you understand what i mean?
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: February 25, 2018
Poll
Do you think parents should charge rent?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.