Question 1

What is sin(270°)?

Accepted Answer

sin(270°) = −1.

This is the minimum value sine can ever reach. On the unit circle, 270° is the point (0, −1) — the very bottom of the circle. The y-coordinate gives sin(270°) = −1.

Sine reaches its minimum of −1 at 270° (and at every 270° + 360°k for integer k). This is directly opposite sin(90°) = 1 — the two extreme values of sine are at the top and bottom of the unit circle.

270° is equivalent to −90° when working with negative angles. sin(−90°) = −1 confirms this.

Question 2

What is cos(270°)?

Accepted Answer

cos(270°) = 0.

At 270°, the unit circle point is (0, −1). The x-coordinate gives cos(270°) = 0.

Cosine is zero at 90° and 270° — both points where the radius is vertical (on the y-axis). These are the zero crossings of cosine.

cos(270°) = cos(−90°) = 0. The cosine function has period 360°, so cos(270°) = cos(270° − 360°) = cos(−90°) = 0.

Note: cos(270°) = sin(180°) = 0 by the identity cos(θ) = sin(θ + 90°) applied carefully.

Question 3

Why is tan(270°) undefined?

Accepted Answer

tan(270°) = sin(270°)/cos(270°) = (−1)/0 — undefined.

Division by zero has no finite answer, so tan(270°) is undefined.

Geometrically: at 270° the radius points straight down — a vertical line. A vertical line has no finite slope, hence tan is undefined.

As the angle approaches 270° from the left (269°, 269.9°...):
tan → +∞

As the angle approaches 270° from the right (271°, 270.1°...):
tan → −∞

Tan has vertical asymptotes at 90°, 270°, 450°... (every odd multiple of 90°) — wherever cos = 0.

Question 4

How does 270° relate to 90°?

Accepted Answer

270° and 90° are directly opposite each other on the unit circle — separated by 180°.

At 90°:  point = (0, 1),  sin = 1,  cos = 0
At 270°: point = (0, −1), sin = −1, cos = 0

The relationships:
- sin(270°) = −sin(90°) = −1
- cos(270°) = cos(90°) = 0 (same)
- csc(270°) = −csc(90°) = −1
- cot(270°) = cot(90°) = 0 (same)
- tan and sec are undefined at both angles

270° is also equivalent to −90°:
- sin(−90°) = −sin(90°) = −1 ✓
- cos(−90°) = cos(90°) = 0 ✓

This makes sense: going 270° counterclockwise is the same as going 90° clockwise.

Question 5

What quadrant is 270° in and what are the sign rules?

Accepted Answer

270° is the boundary between Quadrant III and Quadrant IV — the bottom of the unit circle.

Sign rules by quadrant:
- Q1 (0–90°):   sin+, cos+, tan+
- Q2 (90–180°): sin+, cos−, tan−
- Q3 (180–270°): sin−, cos−, tan+
- Q4 (270–360°): sin−, cos+, tan−

At exactly 270°, sin = −1 (negative, consistent with Q3/Q4) and cos = 0 (the boundary).

For angles just past 270° (entering Q4): cos becomes positive again. For example:
- sin(300°) = −√3/2 (negative)
- cos(300°) = 1/2 (positive, Q4)
- tan(300°) = −√3 (negative, Q4)

Memory trick for quadrant signs: All Students Take Classes
- All (Q1): all positive
- Students (Q2): sine positive
- Take (Q3): tangent positive
- Classes (Q4): cosine positive

NAME	FORMULA	RESULT
Pythagorean identity at 270°	sin²(270°)+cos²(270°) = (−1)²+0² = 1+0	= 1 ✓
Tan(270°) undefined	tan(270°) = sin(270°)/cos(270°) = (−1)/0	= Undefined
Csc(270°)	csc(270°) = 1/sin(270°) = 1/(−1)	= −1
Sec(270°) undefined	sec(270°) = 1/cos(270°) = 1/0	= Undefined
Cot(270°)	cot(270°) = cos(270°)/sin(270°) = 0/(−1)	= 0
Mirror of 90°	sin(270°) = −sin(90°) = −1	270° is 90° reflected through the origin
Minimum of sine	sin(θ) reaches minimum of −1 at θ = 270°	sin(270°) = −1 is the global minimum
Equivalent negative angle	270° = −90° (mod 360°)	sin(−90°) = −1, cos(−90°) = 0

Sin Cos Tan of 270 Degrees — Exact Values

TRIG VALUES AT 270°

UNIT CIRCLE

FORMULAS & IDENTITIES

WORKED EXAMPLE

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

MORE TRIGONOMETRY CALCULATORS

Function	Exact Value	Decimal
sin(270°)	−1	-1
cos(270°)	0	0
tan(270°)	Undefined	—
csc(270°)	−1	-1
sec(270°)	Undefined	—
cot(270°)	0	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