Question

已知等腰三角形的顶角的余弦值等于-7/25,求这个三角形的底角的正弦余弦和正切的值

Answer 1

设底角大小为 θ

则 顶角为 180 - 2θ

cos(180 -2θ) = -7/25

容易判断出 顶角大于90度,而底角为锐角

另外

cos(2θ) = 7/25

1 - 2 (sinθ)^2 = 7/25

(sinθ)^2 = 9/25

(cosθ)^2 = 1 - (sinθ)^2 = 16/25

θ 是锐角,所以

sinθ = 3/5

cosθ = 4/5

tanθ = sinθ/cosθ = 3/4