Cot 345 Degrees

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

What is cot 345°?

Answer

cot 345° =
−2 − √3 ≈ −3.7321

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

≈ — rounded to 4 decimal places.

cot 345° = cot(360° − 15°) = −cot 15° = −2 − √3

cot 345° = cos 345° / sin 345° = ((√6 + √2)/4) / (−(√6 − √2)/4) = −2 − √3

cot 15° = 1 / tan 15° = 1 / (2 − √3) = 2 + √3

xyOP

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

C(cot 345°, 1) ≈ (−3.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed); C is beyond the drawing, the arrow points to it.

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: cot 15° = 2 + √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
330°−√3
341°≈ −2.9042
342°−√(5 + 2√5)
345°−2 − √3
355°≈ −11.4301
360°undefined
390°√3

FAQ

What is cot 345°?

cot 345° = −2 − √3 ≈ −3.7321

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 −1.5425 for cot 345?

The calculator is in radian mode (RAD): it takes cot 345 as the cotangent of 345 radians, cot 345 rad ≈ −1.5425. Switch it to degrees (DEG): cot 345° = −2 − √3 ≈ −3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also