Keys Tan
by admin on Sep.19, 2009, under Leather Wallets For Men
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Keys Tan
Find the exact values of sin(a/2), cos(a/2), tan(a/2)?
Hello everyone;
I am studying for an exam tomorrow. I was able to solve solve sin 2a, cos 2a, tan 2a questions but having problems with this new set.
Here is the question from textbook
"Find the exact values of sin (a/2), cos(a/2), tan(a/2) for the given conditions
sec a = 5/4; O < a < 90. "
The answer given in the answer key is:
1/10 Square Root of 10, 3/10 Square root of 10, 1/3
I will really appreciate if you can explain me how to get this result.
Thanks in advance.
formula
cos(a/2) = √({1 + cos a}/2)
sin(a/2) = √({1 - cos a}/2)
tan(a/2) = sin(a/2)/cos(a/2)
they have positive values since a is in the first quadrant .. . .
0 < a/2 < 45°
as an illustration:
cos a = 4/5
cos(a/2) = √({1 + 4/5} / 2)
= √(9/10) = 3/√10 = 3√10 / 10
the above is the value for cos(a/2) .. . .. .
you can continue with the rest of the values
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| Genuine Leather Zipper Key Chain Holder Wallet #212CF | | | US $6.99 | 26d 5h 52m |
| Super Compact Leather wallet w/ Key Holder #519CF | | | US $7.99 | 28d 26m |
| For Belt TAN Leather MULTI KEY HOLDER WALLET New 1312 | | | US $9.75 | 27d 18h 49m |
| Mens New TAN Leather KEY HOLDER WALLET w/Zip Pocket | | | US $9.25 | 26d 20h 46m |
| NEW DESIGNER KEY WALLET BY LONDON LEATHER IN 5 COLOURS | | | US $18.04 | 26d 3h 53m |
| Eel skin tan tone key holder brass smaller wallet tri fold zipper inside | | | US $8.00 | 23d 21h 11m |
| Budd Leather Classic Leather Goods Zippered Coin Purse with Key Ring Black | | | US $22.99 | 21d 19h 48m |
| New brass genuine leather men's biker wallet chain belt handmade key tan 10mm. | | | US $39.99 | 20d 22h 37m |
| MENS WALLET 1 FLAP CREDIT MONEY PICTURES KEYS NEW TAN | | | US $8.99 | 20d 16h 25m |
| Phantom 1000D Cordura Wallet Key Bag Waist Pack W/Hook - Tan | | | US $21.99 | 19d 3h 24m |
| Clava ID Holder / Key Chain - Bridle Tan | | | US $22.50 | 18d 12h |
| Leather Key Fob / Key Chain by Winn | | | US $13.45 | 15d 7h 33m |
| Leather Key Case Wallet w/ Currency Pocket by Winn | | | US $46.45 | 9d 11h 23m |
| Tri-Fold Cowhide leather wallet Blacks/Browns/Black/Tan with FREE ID Wallet | | | US $9.99 | 1d 7h 11m |
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Taiwanese Dragon Dance (Su-Ti Tan)
How do you calculate inverse sin, cos, and tan without a calculator?
My math book teaches me how to divide the opposite by the adjacent, opposite by the hypotenuse, adjacent by the hypotenuse etc..... this can be done without a calculator. but then it says to figure out the angle you press the inverse sin,cos,tan key on the calculator and it will display the angle. i want to do this without a calculator. i find it fascinating and do take a genuine interest in triangles and how useful they are, but if someday i'm out on a jobsite with no calculator then all this knowledge dont do much for me. i need to be able to do EVERYTHING without a calculator to be happy with myself.THANKS
"i need to be able to do EVERYTHING without a calculator to be happy with myself."
Wow, either you are a spiritual guru, or you have a problem.
At any rate, in the old days, they had tables -- tables of natural trigonometric functions (not logarithmic), tables of logarithmic trigonometric functions, logarithms, etc. With logarithms, you can multiply by adding (you probably know this). There are "Handbooks of Mathematical Tables and Formulas" .
All functions can be calculated with series.
Reconsider -- be happy knowing about tables and how to calculate using series, but keep your calculator. And your computer.
