急! F4 Basic Trigonometry 13q3

Bid

2012-05-02 4:02 pm

請詳細步驟教我計以下幾條 :(不要網址回答) 1. In each of the following, find the quadrant in which the terminal side of θ lines.(d) sinθ/tanθ < 0(e) tanθ/cosθ > 0(f) cosθsinθ < 0 5. Find the values of the following trigonometric ratios without using a calculator.(a) cos300度 (b) tan(-225度)(c) tan 210度 (d) sin135度 11. If tanθ= -20/21 and sinθ<0, find the values of sinθ and cosθ without finding the measure of θ.

回答 (1)

用戶25975

2012-05-02 6:47 pm

✔ 最佳答案

1d) With sin θ/tan θ = cos θ, it will be <0 for quadrants 2 and 3.

e) With tan θ/cos θ = sin θ/cos2 θ, it will be > 0 for quadrants 1 and 2 (sin θ > 0 since cos2 θ > 0 for all θ except 90 and 270)

f) cos θ sin θ < 0 if:

sin θ < 0 and cos θ > 0 (quadrant 4) OR

sin θ > 0 and cos θ < 0 (quadrant 2)

5a) cos 300 = cos (360 - 60) = cos 60 = 1/2

b) tan (-225) = - tan 225 = - tan (180 + 45) = - tan 45 = -1

c) tan 210 = tan (180 + 30) = tan 30 = (√3)/3

d) sin 135 = sin (180 - 45) = sin 45 = (√2)/2

11) tan θ = -20/21 and sin θ < 0, hence cos θ > 0

Thus

sin θ = - 20/√(202 + 212) = -20/29

cos θ = 21/√(202 + 212) = 21/29

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