1. It is given that tanθ = (-9/40) and 3π/2 < θ < 2π. Without using a calculator, find the values of the following expressions.
(a) sin(3π/2 + θ)
(b) cos(π+θ)
(c) sin(θ-13π)
(d) tan(7π/2 - θ)
2. It is given that cosθ = (-5/13) and sinθ < 0. Without using a calculator, find the value of 13sin(θ-270°) / [12cosec(-θ) + 5tan(180°+θ) ].
M2 Trigonometric functions
2015-01-11 8:21 pm
回答 (1)
2015-01-11 9:54 pm
✔ 最佳答案
tanθ = (-9/40)cosθ=40/41
sinθ=-9/41
(a) sin(3π/2 + θ)
= -cos θ
= -40/41
(b) cos(π+θ)
=-cosθ
=-40/41
(c) sin(θ-13π)
=sin(θ-π)
=-sinθ
=9/41
2.
cosθ = (-5/13)
sinθ=-12/13
tanθ=12/5
13sin(θ-270°) / [12cosec(-θ) + 5tan(180°+θ) ]
=13cosθ / [12(-cscθ) + 5tanθ ]
=13(-5/13) / [12(-(-13/12)) + 5(12/5) ]
=-5 / [13 +12]
=-5 / [25 ]
=-1/ 5
2015-01-13 16:54:07 補充：
tan(7π/2 - θ)
=tan(π/2 - θ)
=cotθ
= -40/9
收錄日期: 2021-04-15 17:54:38
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150111000051KK00036