The signs of trigonometric functions by quadrants are determined in accordance with the signs of the points’ coordinates in different quadrants of the coordinate plane.

 

Tips

 

When solving trigonometric problems, you often don’t have enough time to derive all the formulae from scratch, so it would be useful to learn and memorize the signs of trigonometric functions by quadrants.
But if you are confused or unsure whether the sign is correct, you can have a quick check.

Now:

Sine is the axis of ordinates, axis Y.

Cosine is the axis of abscissas, axis X.

If the problem is about the sine of an angle, then:

  • imagine a circle,
  • the angle formed by radius vector OM and the circle,
  • and the sign that the ordinate of point M has, i.e., sign y.

Like the sine, if the problem is about the cosine of an angle,

  • imagine a circle,
  • the angle formed by radius vector OM and the circle,
  • and the sign that the abscissa of point M has, i.e., sign x.

Знаки синуса

The signs of sine

 

 

Знаки косинуса

The signs of cosine