My Math Forum  

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

Trigonometry Trigonometry Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 22nd, 2018, 10:53 AM   #1
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 56
Thanks: 2

Trigonometry identities

I need detailed solutions for the equation
tan^2(x+45)=5 for 0<x<360 where 45 is in degrees.

Last edited by skipjack; August 22nd, 2018 at 11:46 AM.
Harmeed is offline  
 
August 22nd, 2018, 11:45 AM   #2
Global Moderator
 
Joined: Dec 2006

Posts: 19,977
Thanks: 1851

As tan(x + 45$^\circ$) = ±√5, you can calculate possible values for x + 45$^\circ$, namely ±65.9$^\circ$ approximately.

What progress can you make from there?
skipjack is offline  
August 22nd, 2018, 12:45 PM   #3
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 56
Thanks: 2

I don't understand please make it simpler&understandable
Harmeed is offline  
August 22nd, 2018, 06:37 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 19,977
Thanks: 1851

tan²(x+45$^\circ$) = 5 implies tan(x+45$^\circ$) = ±√5.
Do you understand that?
By use of a calculator, tan$^{-1}$(±√5) = ±65.9$^\circ$ approximately.
Do you also understand that?

Are you aware that tan(A) = tan(A ± k(180$^\circ$)) for any integer value of k and any value of A for which tan(A) is defined?
skipjack is offline  
August 22nd, 2018, 10:30 PM   #5
Member
 
Joined: Aug 2018
From: Nigeria

Posts: 56
Thanks: 2

YEAH...proceed please
Harmeed is offline  
August 23rd, 2018, 06:13 AM   #6
Global Moderator
 
Joined: Dec 2006

Posts: 19,977
Thanks: 1851

You need values of x + 45$^\circ\!$ between 45$^\circ\!$ and 405$^\circ\!$, so choose all integer values of k such that ±65.9$^\circ\!$ + k(180$^\circ\!$) is within that range, then you can get the desired (approximate) answers by subtraction of 45$^\circ\!$.

For example, using -65.9 and k = 1 would lead to (-65.9 + 180 - 45)$^\circ\!$, which is 69.1$^\circ\!$.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Trigonometry

Tags
identities, trigonometry



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Trigonometry identities Monokuro Trigonometry 1 May 13th, 2014 02:38 PM
Trigonometry identities Monokuro Trigonometry 1 May 11th, 2014 08:05 AM
Trigonometry - Identities problem tiba Trigonometry 5 May 24th, 2012 08:11 AM
Trigonometry identities hoyy1kolko Algebra 2 March 2nd, 2011 11:49 PM
Trigonometry identities hoyy1kolko Algebra 2 February 26th, 2011 01:43 AM





Copyright © 2018 My Math Forum. All rights reserved.