My Math Forum Stumped simplifying this trig expression

 Trigonometry Trigonometry Math Forum

 October 17th, 2013, 08:45 AM #1 Newbie   Joined: Mar 2013 Posts: 24 Thanks: 0 Stumped simplifying this trig expression Need help simplifying! The answer key in my book swears I can simplify this further, but I don't see how! sin(arcsec(-5))cos(arcsec(-5)) There is an exact answer, but I can't arrive there unless I know the angle in radians... but this is not a common angle and I have no clue how to go about this.
 October 17th, 2013, 09:34 AM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,968 Thanks: 1152 Math Focus: Elementary mathematics and beyond Re: Stumped simplifying this trig expression I get -2?(6)/25. Construct a right triangle with hypotenuse 5, adjacent side 1 and opposite side ?(5² - 1²) = 2?(6). The cosine of this triangle is 1/5 and the sine is 2?(6)/5, so we start with 2?(6)/5 * 1/5 = 2?(6)/25. To account for the sign, we have that arcsec(5) = arccos(1/5), but we have arcsec(-5) = arccos(-1/5), so cos(arccos(-1/5)) = -1/5. The range of the arccos function is [0, ?], hence sin(arccos(-1/5)) is positive, giving us 2?(6)/5 * -1/5 = -2?(6)/25. One could initially assume the identity arcsec(x) = arccos(1/x) and proceed in a fashion similar to the above. http://en.wikipedia.org/wiki/Inverse_tr ... _functions

 Tags expression, simplifying, stumped, trig

### simplify arcsin

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post finmorhouse Algebra 3 October 8th, 2012 11:27 PM daigo Trigonometry 7 June 30th, 2012 11:31 AM Gustav Algebra 1 October 10th, 2010 12:51 AM paulw Applied Math 3 September 23rd, 2010 11:22 AM finmorhouse Linear Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top