Turn on thread page Beta
 You are Here: Home >< Maths

# Trig question watch

1. The graphs of y=cos^-1(x) and
y=tan^-1(x), where x lies between 1 and -1 in each case.

The graphs intersect at the point with
coordinates (p,q).

Write down, in terms of p and q,the
coordinates of the corresponding point of

intersection of the graphs of y=cosx
and y=tanx, and hence show that

cos^2(q)=sinq. This is the question I
tried and couldnt do will appreciate if
someone helps me out with this.
2. Here's my take on it:
y=cos^-1(x) => x=cos(y) ,
y=tan^-1(x) => x=tan(y)
x=tan(y)=cos(y) where they intersect.
trig identities: Sin(y)/cos(y)=tan(y) => sin(y)/cos(y)=cos(y) => sin(y)= cos^2(y)
and where they intersect p is the y coordinate, so just put the p in place of the y.
Dunno about this corresponding point mumbo jumbo, wouldn't it just be (q,p)?
3. Ok, so, you know cos^-1x=y and tan^-1x=y.

=> cosy=x (1) and tany=x (2)

Sub (1) into (2):

=>cosy=tany

=>cosy=siny/cosy

Does this help?
4. (Original post by TheSK00T3R)
Here's my take on it:
y=cos^-1(x) => x=cos(y) ,
y=tan^-1(x) => x=tan(y)
x=tan(y)=cos(y) where they intersect.
trig identities: Sin(y)/cos(y)=tan(y) => sin(y)/cos(y)=cos(y) => sin(y)= cos^2(y)
and where they intersect p is the y coordinate, so just put the p in place of the y.
Dunno about this corresponding point mumbo jumbo, wouldn't it just be (q,p)?
Just ignore the word "corresponding"

Turn on thread page Beta
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:
Updated: November 18, 2013
Today on TSR

### Cambridge interviews

Find out which colleges are sending invitations

### University open days

• University of East Anglia
UEA Mini Open Day Undergraduate
Fri, 23 Nov '18
• Norwich University of the Arts
Fri, 23 Nov '18
• Edge Hill University
Sat, 24 Nov '18
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

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