马上就要迎来了欧几里得考试了，本期想来给同学讲解的是欧几里得考点之一的三角函数，下面就来看看有哪些公式和值得看的例题！
SINE law
Cosine Law
a^2 = b^2 + c^2 − 2bc cos A
b^2 = a^2 + c^2 − 2ac cos B
c^2 = b^2 + a^2 − 2ab cos C
Area relations
The area of triangle ABC = |4ABC| = 1/2 ab sin C = 1/2 bc sin A = 1/2 ac sin B.
Area of an equilateral triangle
The area of an equilateral triangle of side length s is
Heron’s formula
Trigonometric Identities
Related Angle Identities
sin(180◦ − θ) = sin θ cos(180◦ − θ) = − cos θ
Draw graphs of
y = A sin(kx + d)
y = A cos(kx + d)
y = tan x
例题
An airplane leaves an aircraft carrier and flies due south at 400 km/hr. The carrier proceeds at a heading of 60◦ west of north at 32 km/hr. If the plane has 5 hours of fuel, what is the maximum distance south the plane can travel so that the fuel remaining will allow a safe return to the carrier at 400 km/hr?
解析：
The first step in solving this problem is to draw a diagram (as shown). If we let x be the number of hours that the plane flies south then the distance that the plane flies south is 400x. The plane then flies a distance 400(5 − x). in the remaining time while the total distance the carrier flies is 5(32). Using these distances the cosine law states: (400(5 − x))2 = 1602 + (400x) 2 − 2 · 160 · 400x · cos 120◦ .
像欧几里得这类的国际竞赛不像学校里的考试那样，有很多固定的套路，会非常考验你的创造力和灵活的思维能力，如果感觉一个人摸索复习有点孤单，可以点击预约试听【唯寻欧几里得竞赛班课】——
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