Explanations
45° - Special Angle
45° creates a perfect diagonal, bisecting a right angle. sin(45°) = cos(45°) = √2/2, tan(45°) = 1. This angle is fundamental in isosceles right triangles and creates equal x and y components.
First Quadrant (I)
In Quadrant I, both x and y coordinates are positive. All trigonometric functions (sin, cos, tan) are positive here. This quadrant contains angles from 0° to 90° and represents the 'northeast' section of the coordinate plane.
Reference Angle
A reference angle is the acute angle between the terminal ray and the x-axis. It's always between 0° and 90° and helps determine the sign and magnitude of trigonometric functions. Reference angles make calculations easier by relating any angle to a familiar acute angle.
Trigonometric Functions
The six trigonometric functions relate angles to ratios in right triangles and positions on the unit circle. Sine (sin) represents the y-coordinate, cosine (cos) the x-coordinate, and tangent (tan) the ratio y/x. The reciprocal functions are cosecant (csc), secant (sec), and cotangent (cot).