Exact
√2/2
Cos 45 Degrees
Answer
cos 45° equals √2/2, which is 0.7071067812 as a decimal.
Decimal
0.7071067812
Formula
cos 45° = √2/2 = 0.7071067812
Worked steps
1
Right-triangle definition
In a right triangle, cos(angle) = adjacent side ÷ hypotenuse. For a 45° angle in a right isosceles triangle, cos 45° = √2/2.
2
Calculator method (DEG mode)
Set the calculator to DEG. Press cos, type 45, press =. Result: 0.7071067812.
3
Calculator method (RAD mode)
Convert 45° to radians first: 45 × π / 180 = 0.785398 rad. Then cos of that gives 0.7071067812.
About this value
Cos 45° is a standard trigonometric value. The exact form is √2/2; the decimal 0.7071067812 is what a calculator returns. Notice it equals sin 45° — at 45°, sin and cos are the same.
Frequently asked questions
What is cos 45 degrees?
Cos 45 Degrees equals √2/2 as an exact value, or 0.7071067812 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 45° is 0.7071067812 in DEG or sin(angle_in_rad) of the equivalent radian measure.