Q.Find all trigonometric functions of the angle in standard position whose terminal arm passes through the point $(3, −4)$.

For an acute angle inside a right triangle, sinθ, cosθ and tanθ are ratios of sides. To make sense of trigonometric functions for any real angle θ — including obtuse, negative, or angles larger than 360° — we place θ in standard position: vertex at the origin O, initial ray along the positive x-axis. Its terminal ray meets a circle of radius r centred at O in a unique point P(x, y). We then define

$\cos\theta = \frac{x}{r}, \qquad \sin\theta = \frac{y}{r}, \qquad \tan\theta = \frac{y}{x}\ (x \neq 0)$ …