Trigonometric functions
Radians, all four quadrants, and values beyond 90°.
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Walk round a circle of radius 1: cos tells how far across you are, sin how far up.
Look: At 120°: across −0.5 (left), up 0.87.
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1cos 180° = ?
2sin 90° = ?
3π/3 in degrees?
! Careful!
✗sin and cos are always positive.
✓On the left side cos is negative; below, sin is negative.
✗Mixing degrees and radians on a calculator.
✓Check the calculator mode.
See the whole lesson on one page
Walk round a circle of radius 1: cos tells how far across you are, sin how far up.
Turn by an angle from the right-hand side. The point you reach is (cos θ, sin θ). Left of centre, cos is negative. Below, sin is negative.
Think of it like thisRide a giant wheel. As it turns, your height goes up and down smoothly. That up-and-down wave is the sine curve.
- Radian
- Another angle unit: π radians = 180°.
Solved together
Find sin 150° and cos 150°.
150° is 30° short of 180°. So it looks like 30°, but on the left side.
Up is still positive. Across is now negative.
sin 150° = sin 30° = ½cos 150° = −cos 30° ≈ −0.87
Answersin 150° = ½, cos 150° ≈ −0.87.
For older learners and grown-ups: a little more
sin and cos repeat every 360° (2π). Signs by quadrant: All positive (I), Sin (II), Tan (III), Cos (IV).
Now practise it
Kanakku makes new questions on trigonometric functions every time. It shows the working and gives a hint when you are stuck.