Question 1

What is sin(0°)?

Accepted Answer

sin(0°) = 0.

Explanation: On the unit circle, 0 degrees corresponds to the point (1, 0) on the positive x-axis. The y-coordinate of this point is the sine value. Since the y-coordinate is 0, sin(0°) = 0.

In a right triangle, sin(theta) = opposite / hypotenuse. As the angle approaches 0, the opposite side shrinks to zero while the hypotenuse stays fixed, so sin approaches 0.

Verification: sin²(0°) + cos²(0°) = 0² + 1² = 0 + 1 = 1 ✓

Question 2

What is cos(0°)?

Accepted Answer

cos(0°) = 1.

Explanation: At 0 degrees, the point on the unit circle is (1, 0). The x-coordinate is the cosine value. Since x = 1, cos(0°) = 1.

In a right triangle, cos(theta) = adjacent / hypotenuse. At angle 0, the triangle collapses and the adjacent side equals the hypotenuse, giving a ratio of 1.

cos(0°) = 1 is the maximum possible value of cosine. Cosine decreases from 1 to -1 as the angle goes from 0° to 180°.

Question 3

What is tan(0°)?

Accepted Answer

tan(0°) = 0.

Explanation: tan = sin/cos = 0/1 = 0.

Alternatively, in a right triangle, tan = opposite/adjacent. At 0 degrees, the opposite side has length 0, so the ratio is 0/adjacent = 0 regardless of the adjacent length.

Compare: tan(45°) = 1 (equal sides), tan(90°) = undefined (vertical line, infinite slope). Tan(0°) = 0 makes sense — it is the slope of a horizontal line.

Question 4

Why are csc(0°) and cot(0°) undefined?

Accepted Answer

csc(0°) = 1/sin(0°) = 1/0, which is undefined. Division by zero is not a valid operation in mathematics.

cot(0°) = cos(0°)/sin(0°) = 1/0, also undefined for the same reason.

As the angle approaches 0 from above (tiny positive angles):
- csc approaches positive infinity
- cot approaches positive infinity

As the angle approaches 0 from below (tiny negative angles near 360°):
- csc approaches negative infinity
- cot approaches negative infinity

This is why csc and cot have vertical asymptotes at 0°, 180°, and 360° — anywhere that sin = 0.

Question 5

Why does the unit circle point at 0° equal (1, 0)?

Accepted Answer

The unit circle is a circle of radius 1 centred at the origin. Any point on it is at distance 1 from the origin.

Angles are measured counterclockwise from the positive x-axis. At 0 degrees, you have not rotated at all — you are exactly on the positive x-axis.

The point on the positive x-axis at distance 1 from the origin is (1, 0).

Since any point on the unit circle has coordinates (cos θ, sin θ):
- cos(0°) = x-coordinate = 1
- sin(0°) = y-coordinate = 0

All other angle values can be understood the same way: 90° gives the top of the circle (0, 1), 180° gives the leftmost point (-1, 0), 270° gives the bottom (0, -1), and 360° brings you back to (1, 0).

°	sin	cos	tan
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3
90°	1	0	Undef
120°	√3/2	−1/2	−√3
135°	√2/2	−√2/2	−1
150°	1/2	−√3/2	−1/√3
180°	0	−1	0
270°	−1	0	Undef
360°	0	1	0

NAME	FORMULA	RESULT
Pythagorean identity at 0°	sin²(0)+cos²(0) = 0²+1² = 0+1 = 1	= 1 ✓
Tan from sin/cos	tan(0°) = sin(0°)/cos(0°) = 0/1	= 0
Csc undefined	csc(0°) = 1/sin(0°) = 1/0	= Undefined (division by zero)
Sec at 0°	sec(0°) = 1/cos(0°) = 1/1	= 1
Cot undefined	cot(0°) = cos(0°)/sin(0°) = 1/0	= Undefined (division by zero)
Double angle (sin)	sin(2×0°) = 2·sin(0°)·cos(0°) = 0	= 0
Double angle (cos)	cos(2×0°) = cos²(0°)−sin²(0°) = 1	= 1
Complement	sin(0°) = cos(90°), cos(0°) = sin(90°)	Co-function identities

Sin Cos Tan of 0 Degrees — Exact Values

TRIG VALUES AT 0°

UNIT CIRCLE

FORMULAS & IDENTITIES

WORKED EXAMPLE

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

MORE TRIGONOMETRY CALCULATORS

Function	Exact Value	Decimal
sin(0°)	0	0
cos(0°)	1	1
tan(0°)	0	0
csc(0°)	Undefined	—
sec(0°)	1	1
cot(0°)	Undefined	—