My Math Forum Trigonometry identities

 Trigonometry Trigonometry Math Forum

 August 22nd, 2018, 09:53 AM #1 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 Trigonometry identities I need detailed solutions for the equation tan^2(x+45)=5 for 0
 August 22nd, 2018, 10:45 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 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?
 August 22nd, 2018, 11:45 AM #3 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 I don't understand please make it simpler&understandable
 August 22nd, 2018, 05:37 PM #4 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 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?
 August 22nd, 2018, 09:30 PM #5 Member   Joined: Aug 2018 From: Nigeria Posts: 73 Thanks: 2 YEAH...proceed please
 August 23rd, 2018, 05:13 AM #6 Global Moderator   Joined: Dec 2006 Posts: 20,919 Thanks: 2203 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$^\circ\!$.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Monokuro Trigonometry 1 May 13th, 2014 01:38 PM Monokuro Trigonometry 1 May 11th, 2014 07:05 AM tiba Trigonometry 5 May 24th, 2012 07:11 AM hoyy1kolko Algebra 2 March 2nd, 2011 10:49 PM hoyy1kolko Algebra 2 February 26th, 2011 12:43 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top