Reference Angle Calculator
The reference angle calculator finds the corresponding angle in the first quadrant.
The rule
the acute angle between the terminal side and the x-axis
What a reference angle is for
Trigonometric values repeat around the circle up to sign, so any angle’s sine, cosine and tangent match those of its reference angle — the acute angle it makes with the x-axis — with a sign set by the quadrant. That turns every trig value into one you already know from the first quadrant.
Degrees and radians
A full turn is 360° or 2π radians, so:
radians = degrees × π/180 and degrees = radians × 180/π
Degrees are convenient because 360 divides so many ways. Radians are the natural choice in mathematics because arc length becomes simply rθ and the calculus of sine and cosine comes out clean — derivatives pick up stray factors of π/180 in degrees.
Names worth knowing
- Acute — under 90°. Right — exactly 90°. Obtuse — between 90° and 180°.
- Straight — 180°. Reflex — over 180°.
- Complementary pairs add to 90°; supplementary pairs add to 180°.