高考数学：三角函数基础
A high-school mathematics practice set on trigonometric function fundamentals: radian measure, definitions via coordinates, the fundamental Pythagorean identity, co-function/reduction formulas, and periodicity of sine and cosine functions.
- Convert between degree and radian measure
- Apply the fundamental trigonometric identity sin^2+cos^2=1
- Use reduction formulas to simplify trigonometric expressions
- Determine the period and monotonicity of basic trigonometric functions
高考数学：三角函数基础 — 弧度制、三角函数值、同角关系、诱导公式与基础图像性质。
示例问题
已知角 $\alpha$ 的终边经过点 $P(3, -4)$，则 $\sin \alpha$ 的值为多少？
- $\frac{3}{5}$
- $\frac{4}{5}$
- $-\frac{4}{5}$
- $-\frac{3}{5}$
查看答案
$-\frac{4}{5}$
根据三角函数定义，点 $P(x, y)$ 的坐标为 $(3, -4)$，则半径 $r = \sqrt{x^2 + y^2} = \sqrt{3^2 + (-4)^2} = 5$。因此 $\sin \alpha = \frac{y}{r} = \frac{-4}{5}$。