Trigonometric Functions: Trigonometric Values in All Four Quadrants

Using Special Right Triangles

Let’s put all of the information we have leaned thus far to find the cosine and sine of 45°.

We can build the following right triangle:

P(cos 45°, sin 45°)

= 45-45-90 degree triangle with legs equal to 1 and hypotenuse equal to square root of 2

cosine of 45 degrees equals 1 divided by square root of 2 equals 1 divided by square root of 2 times square root of 2 divided by square root of 2 equals square root of 2 divided by square root of 4 equals square root of 2 divided by 2

sine of 45 degrees equals 1 divided by square root of 2 equals 1 divided by square root of 2 times square root of 2 divided by square root of 2 equals square root of 2 divided by square root of 4 equals square root of 2 divided by 2

You have now found one point on the unit circle.

45 Degrees on the Unit Circle