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9 months ago

Olympiad 3

Olympiad

Mathematics Sec4 Trigonometry, grade 10 DY Chan Eng March 3, 2018 Exercise 1. Given that tan A = − 8 15 and that π < A < π, find the value of 2 cos A and of sin A. Exercise 2. Ginven that sin B = −√ 2 and that π 5 2 < B < 3π , find the value 2 of cot B. Exercise 3. Aircraft Navigation. In the planning of a flight schedule, a pilot must calculate the ground speed, v km/h, of the plane by taking into account the speed and direction of the wind. The ground speed in km/h can be express as 770 sin 135◦ v = sin θ Without calculate, find the value of v if tan θ = 7 and 0 ◦ < θ < 180 ◦ ( Exercise 4. Show that sin θ k cot θ, where k is a constant. 2 1 − cos θ − 2 1 + cos θ ) can be expressed as Exercise 5. Given 3 cos α = x and 2 tan α = y. Express sin α in terms of x and y, hence or otherwise, evaluate 4x 2 + x 2 y 2 . Exercise 6. Prove that (sec x + tan x)(sec x − tan x) + (csc x + cot x)(csc x − cot x) = 2 Notation: sec x = 1 cos x (secant) and csc x = 1 sin x 1 (cosecant) or cosec x

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