Problem about Trig.

👨🏻‍🏫 學術台數學

用戶249547

2008-05-23 9:54 pm

Given sinA = (3/5), A in quadrant II, and cosB = (7/25), B in quadrant I.
Please find the follows...
1) sin(A+B)
2) cos(2A)
3) sin(A/2)

Thank you~

更新1:

The List of Equations: http://img373.imageshack.us/img373/7171/20080522003bn0.jpg

回答 (1)

Chui Ling

2008-05-23 10:09 pm

✔ 最佳答案

1. sin(A+B) =sinAcosB+cosAsinB
cosA=-4/5
sinB=24/25
so sin(A+B) =(3/5)(7/25)+(-4/5)(24/25)
=-3/5

2.cos(2A)=1-2sin^2 A
=1-2*(3/5)^2
=7/25

3.cos(2A)=1-2sin^2 A
so cos(A)=1-2sin^2 (A/2)
-4/5 = 1- 2sin^2 (A/2)
2sin^2 (A/2)=1+4/5
sin^2 (A/2)=0.9
sin(A/2)=3/ (sq rt 10) or -3/ (sq rt 10) (reject)
-3/ (sq rt 10) reject since when we finding A/2, it is in quadrant I

參考: my math knowledge

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