1. Sue was born on a Saturday on May 10, 1986. What day of the week will her 20 th birthday fall on?
2. Two chords of a circle, WX and YZ, intersect at point P outside of the circle. Let WX=5, XP=3, YZ=10. Find ZP, where YZ+ZP=YP.
3. An identity for cot(x-135 degrees) is?
The answer is (cosx-sinx)/(sinx+cosx)..but why???
幾條中3數學題...help plz
2007-03-17 1:30 pm
回答 (2)
2007-03-17 1:49 pm
✔ 最佳答案
1.Denote Sunday, Monday, ... Saturday by 0, 1, ..., 6
# of leap years = floor(20/4) = 5
(leap years: 1988, 1992, 1996, 2000, 2004)
Day = (6 + floor(20/4) * 366 + (20 - floor(20/4)) * 365) mod 7 = 3 = Wednesday
2. The chord theorem states that if two chords, WX and YZ, intersect at P, then WP * XP = YP * ZP. (Chord theorem)
WP * XP = YP * ZP
(5+3) * 3 = ZP * (10 + ZP)
ZP^2 + 10 * ZP - 24 = 0
ZP = 2 or - 12(rejected)
3.
cot(x - 135)
= cos(x - 135) / sin(x - 135)
= (cos x cos 135 + sin x sin 135) / (sin x cos 135 - cos x sin 135)
= (cos x cos 135 - sin x cos 135) / (sin x cos 135 + cos x cos 135)
= (cos x - sin x) / (sin x + cos x)
sin(A-B)=sin A cos B - cos A sin B
cos(A-B)=cos A cos B + sin A sin B
(from http://en.wikibooks.org/wiki/Trigonometry/Sum_and_Difference_Formulas)
sin 135 = -cos 135 = 1 / sqrt(2)
(from Calculator)
2007-03-17 4:16 pm
1.Denote Sunday, Monday, ... Saturday by 0, 1, ..., 6
# of leap years = floor(20/4) = 5
(leap years: 1988, 1992, 1996, 2000, 2004)
Day = (6 + floor(20/4) * 366 + (20 - floor(20/4)) * 365) mod 7 = 3 = Wednesday
# of leap years = floor(20/4) = 5
(leap years: 1988, 1992, 1996, 2000, 2004)
Day = (6 + floor(20/4) * 366 + (20 - floor(20/4)) * 365) mod 7 = 3 = Wednesday
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