Cos 45 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is cos 45°?

Answer

cos 45° =
√2/2 ≈ 0.7071

Angle in radians: 45° = π/4. The point of the angle is in quadrant I, where cosine is positive.

≈ — rounded to 4 decimal places.

P(cos 45°, sin 45°) = (√2/2, √2/2)

An isosceles right triangle with legs 1: the hypotenuse is √2.

cos 45° = 1/√2 = √2/2

xyOP

P(cos 45°, sin 45°) ≈ (0.7071, 0.7071)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.7071.

All four functions of 45°
FunctionExact valueDecimal
sin 45°√2/2≈ 0.7071
cos 45°√2/2≈ 0.7071
tan 45°11
cot 45°11

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
42°≈ 0.7431
43°≈ 0.7314
44°≈ 0.7193
45°√2/2
46°≈ 0.6947
47°≈ 0.6820
48°≈ 0.6691

FAQ

What is cos 45°?

cos 45° = √2/2 ≈ 0.7071

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cos 45° = √2/2 ≈ 0.7071.

Why does a calculator show 0.5253 for cos 45?

The calculator is in radian mode (RAD): it takes cos 45 as the cosine of 45 radians, cos 45 rad ≈ 0.5253. Switch it to degrees (DEG): cos 45° = √2/2 ≈ 0.7071. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also