Exact
√3/2
Cos 30 Degrees
Answer
cos 30° equals √3/2, which is 0.8660254038 as a decimal.
Decimal
0.8660254038
Formula
cos 30° = √3/2 = 0.8660254038
Worked steps
1
Right-triangle definition
In a right triangle, cos(angle) = adjacent side ÷ hypotenuse. For a 30°–60°–90° triangle, the adjacent side at the 30° angle gives cos 30° = √3/2.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press cos, type 30, press =. Result: 0.8660254038.
3
Calculator method (RAD mode)
Convert 30° to radians first: 30 × π / 180 = 0.523599 rad. Then cos of that gives 0.8660254038.
About this value
Cos 30° is a standard trigonometric value. The exact form is √3/2; the decimal 0.8660254038 is what a calculator returns. Notice it equals sin 60° — cosine and sine are complementary.
Frequently asked questions
What is cos 30 degrees?
Cos 30 Degrees equals √3/2 as an exact value, or 0.8660254038 as a decimal. The exact form is what you'd typically write in exam working; the decimal is what your calculator displays.
How do I enter this on a calculator?
Set the angle mode to DEG. Press cos, type the angle, press =. If your calculator is in RAD mode by mistake, you will get a different answer — always check the mode pill before pressing a trig function.
Why memorise the standard angle values?
The values for 30°, 45°, 60°, and 90° appear in almost every trigonometry problem at school level. Knowing the exact form (with surds) lets you produce surd-form answers expected in exams, instead of decimal approximations.
What is this in radians?
To convert the angle to radians, multiply by π/180. The function value is the same regardless of mode — the answer for 30° is 0.8660254038 in DEG or sin(angle_in_rad) of the equivalent radian measure.