F.2 maths(trigonmetric relations) very easy...(10marks)

2008-05-28 1:37 am

1.
If sinA=7/25, find the values of cosA and tan A.

2.
Given that tanθ=3/2, and find the value of [(1/sinθ)-sinθ]x(1/cosθ)

3.
Express (cos42)/(cos48) in the form tanθ.

4.
Express (cos33)/(tan57) in the form sinθ.

5.
Express tan15sin75 in the form cosθ.

以上題目請不要使用計算機, 要列清楚步驟, thx!!

回答 (1)

用戶7639

2008-05-28 2:08 am

✔ 最佳答案

1.
If sinA=7/25, find the values of cosA and tan A.

cosA=24/25
tanA=7/24
2.
Given that tanθ=3/2, and find the value of [(1/sinθ)-sinθ]x(1/cosθ)

[(1/sinθ)-sinθ]x(1/cosθ)
=(1-sin2θ)/sinθ x (1/cosθ)
=cos2θ/sinθ x (1/cosθ)
=cos/sinθ
=1/tanθ
=1/(3/2)
=2/3
3.
Express (cos42˚)/(cos48˚) in the form tanθ.

(cos42˚)/(cos48˚)
=[sin(90˚-42˚)] /cos48˚
=sin48˚/cos48˚
=tan48˚
4.
Express (cos33˚)/(tan57˚) in the form sinθ.

(cos33˚)/(tan57˚)
=cos33˚/cot(90˚-57˚)
=cos33˚/cot33˚
=sin33˚
5.
Express tan15˚sin75˚ in the form cosθ.

tan15˚sin75 ˚
=tan(90˚-15˚)sin75˚
=cot75˚sin75˚
=cos75˚

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