My Math Forum  

Go Back   My Math Forum > High School Math Forum > Trigonometry

Trigonometry Trigonometry Math Forum


Thanks Tree3Thanks
Reply
 
LinkBack Thread Tools Display Modes
August 22nd, 2018, 08:16 AM   #1
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 43
Thanks: 2

Trigonometry

Given tan(x-y)=-2/3 and tanx=-1/2, find the value of
a. tan y
b. (x+y) for 0<x+y<360

please. I need all possible solutions.

Last edited by skipjack; August 22nd, 2018 at 10:20 AM.
Harmeed is offline  
 
August 22nd, 2018, 08:24 AM   #2
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,204
Thanks: 511

Math Focus: Calculus/ODEs
A well-known identity (angle-difference for tangent) tells us:

$\displaystyle \tan(x-y)=\frac{\tan(x)-\tan(y)}{1+\tan(x)\tan(y)}$

So, equate this to the given value, and substitute for $\displaystyle \tan(x)$ to get:

$\displaystyle \frac{-\dfrac{1}{2}-\tan(y)}{1-\dfrac{1}{2}\tan(y)}=-\frac{2}{3}$

Now, solve for $\displaystyle \tan(y)$.
MarkFL is offline  
August 22nd, 2018, 08:55 AM   #3
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 43
Thanks: 2

final answer.... please
Harmeed is offline  
August 22nd, 2018, 09:02 AM   #4
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,204
Thanks: 511

Math Focus: Calculus/ODEs
Quote:
Originally Posted by Harmeed View Post
final answer.... please
I'm trying to help you find the answer, not just do your homework for you. That doesn't help you learn.
Thanks from jonah and greg1313
MarkFL is offline  
August 22nd, 2018, 09:20 AM   #5
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 43
Thanks: 2

But I obtained -3-3y/2, but my textbook says 1/8. I need full workings.

Last edited by skipjack; August 22nd, 2018 at 09:51 AM.
Harmeed is offline  
August 22nd, 2018, 09:42 AM   #6
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,204
Thanks: 511

Math Focus: Calculus/ODEs
Quote:
Originally Posted by Harmeed View Post
But I obtained -3-3y/2, but my textbook says 1/8. I need full workings.
Without seeing your actual work, I have no idea what you did wrong, and the expression you supplied makes no sense either, since it is not an equation.

Let's let $\displaystyle u=\tan(y)$ and write:

$\displaystyle \frac{-\dfrac{1}{2}-u}{1-\dfrac{1}{2}u}=-\frac{2}{3}$

Multiply both sides by $\displaystyle -1$:

$\displaystyle \frac{\dfrac{1}{2}+u}{1-\dfrac{1}{2}u}=\frac{2}{3}$

Multiply the LHS by $\displaystyle \frac{2}{2}$:

$\displaystyle \frac{1+2u}{2-u}=\frac{2}{3}$

Multiply through by $\displaystyle 3(2-u)$:

$\displaystyle 3(1+2u)=2(2-u)$

Distribute:

$\displaystyle 3+6u=4-2u$

Collect like terms:

$\displaystyle 8u=1$

Divide through by 8 to obtain:

$\displaystyle u=\tan(y)=\frac{1}{8}$

To do part b), use the angle sum identity for tangent, and use the now known values of $\displaystyle \tan(x)$ and $\displaystyle \tan(y)$ to get a numerical value of $\displaystyle \tan(x+y)$, from which you can deduce the possible values of the angle $\displaystyle x+y$ on the given interval.

This time, please show each step of your work.
Thanks from greg1313

Last edited by skipjack; August 22nd, 2018 at 09:51 AM.
MarkFL is offline  
August 22nd, 2018, 09:54 AM   #7
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,204
Thanks: 511

Math Focus: Calculus/ODEs
skipjack...why are you editing my posts?
MarkFL is offline  
August 22nd, 2018, 09:56 AM   #8
Global Moderator
 
Joined: Dec 2006

Posts: 19,703
Thanks: 1804

Because I edited the post you quoted.
skipjack is offline  
August 22nd, 2018, 09:58 AM   #9
Senior Member
 
MarkFL's Avatar
 
Joined: Jul 2010
From: St. Augustine, FL., U.S.A.'s oldest city

Posts: 12,204
Thanks: 511

Math Focus: Calculus/ODEs
Quote:
Originally Posted by skipjack View Post
Because I had edited the post you quoted.
Okay...I notice many of my posts get edited by you, and I've been curious about it. Today, I decided to inquire.
MarkFL is offline  
August 22nd, 2018, 10:07 AM   #10
Global Moderator
 
Joined: Dec 2006

Posts: 19,703
Thanks: 1804

As tan(y) = tan(x - (x - y)), expand the right-hand side by using the tangent of angle-difference formula once, then substitute the values given for tan(x - y) and tan(x) and evaluate the result. Can you also post your work?

After tan(y) has been found, expand tan(x + y) in terms of tan(x) and tan(y), then substitute the values of tan(x) and tan(y). Use this result to find a possible value (in degrees, to an appropriate number of decimal places) of x + y. To find values in the specified range, add or subtract integer multiples of 180 degrees.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
trigonometry



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Trigonometry John Marsh Trigonometry 3 September 6th, 2013 02:27 AM
Trigonometry Help kiyoshi7 Trigonometry 3 August 29th, 2013 08:30 AM
Trigonometry johnny Algebra 6 March 7th, 2011 01:06 PM
Trigonometry johnny Algebra 7 March 5th, 2011 08:39 AM
trigonometry willab Algebra 2 October 11th, 2010 01:11 PM





Copyright © 2018 My Math Forum. All rights reserved.