Cos 345 Degrees

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

What is cos 345°?

Answer

cos 345° =
(√6 + √2)/4 ≈ 0.9659

Angle in radians: 345° = 23π/12. The point of the angle is in quadrant IV, where cosine is positive.

≈ — rounded to 4 decimal places.

cos 345° = cos(360° − 15°) = cos 15° = (√6 + √2)/4

P(cos 345°, sin 345°) = ((√6 + √2)/4, −(√6 − √2)/4)

cos 15° = cos(45° − 30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4

xyOP

P(cos 345°, sin 345°) ≈ (0.9659, −0.2588)

Highlighted: the projection on the x-axis — cosine, x ≈ 0.9659.

All four functions of 345°
FunctionExact valueDecimal
sin 345°−(√6 − √2)/4≈ −0.2588
cos 345°(√6 + √2)/4≈ 0.9659
tan 345°√3 − 2≈ −0.2679
cot 345°−2 − √3≈ −3.7321

Reference angle: cos 15° = (√6 + √2)/4

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
330°√3/2
341°≈ 0.9455
342°√(10 + 2√5)/4
345°(√6 + √2)/4
355°≈ 0.9962
360°1
390°√3/2

FAQ

What is cos 345°?

cos 345° = (√6 + √2)/4 ≈ 0.9659

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show 0.8391 for cos 345?

The calculator is in radian mode (RAD): it takes cos 345 as the cosine of 345 radians, cos 345 rad ≈ 0.8391. Switch it to degrees (DEG): cos 345° = (√6 + √2)/4 ≈ 0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also