Trigonometry Table & Unit Circle
Exact values of all six ratios for every standard angle from 0° to 360°, a unit circle you can drag, a calculator for any angle and a cheat sheet you can print with your name.
The trigonometry table gives exact ratios for the standard angles. sin 0°, 30°, 45°, 60°, 90° are 0, 1/2, 1/√2, √3/2, 1; cos runs the same list backwards; and tan θ = sin θ ÷ cos θ, so tan 60° = √3. tan 90° is not defined because cos 90° = 0.
Trigonometric ratios, 0° to 90°
Tap any angle to show it on the unit circle. “Not defined” means the ratio would divide by zero.
Interactive unit circle
Drag the red point (or use the slider / arrow keys).
Any-angle calculator
Works for negative angles, angles above 360° and radians like 2π/3.
Remember the table in 4 steps
Step 1: write 0, 1, 2, 3, 4 under 0°, 30°, 45°, 60°, 90°.
ASTC — “All Students Take Chocolate”
Going anticlockwise from Quadrant I: All ratios are positive, then only Sin, then only Tan, then only Cos (with their reciprocals).
To find sin, cos or tan of any angle: find the reference angle (the acute angle to the x-axis), take the value from the 0°–90° table and attach the sign from ASTC. Example: cos 120° = −cos 60° = −½.
Trigonometric identities
The ones you need for Class 10 boards and Class 11–12. Tap an identity to copy it.
Your cheat sheet
Uses the range and value style chosen above. Add your name to personalise it.
Six ratios, one circle
Every trigonometric value comes from a point on a circle of radius 1 — the table is just that circle written down.
Pick a range
0°–90° for Class 10, or extend to 180° and 360° for Class 11.
Exact or decimal
Keep surds like √3/2 for exams, or switch to decimals to check calculator answers.
Drag the circle
See sin, cos and tan as real line segments and watch the signs change by quadrant.
Print and revise
Download or print the cheat sheet with your name for quick revision.
The six ratios
In a right triangle with angle θ: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent.
cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ. Memory aid: “SOH CAH TOA”.
On the unit circle
The point at angle θ on a circle of radius 1 is (cos θ, sin θ). So sin θ is the height of the point and cos θ is its distance across.
tan θ = sin θ ÷ cos θ is the length cut on the tangent line x = 1.
Why “not defined”?
tan 90° = sin 90° ÷ cos 90° = 1 ÷ 0, and division by zero is not allowed. The same happens to sec 90°, cosec 0° and cot 0°.
Radians: 180° = π rad, so 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2.
Trigonometry Table & Unit Circle — your questions
How do I remember the trigonometry table?
Write 0, 1, 2, 3, 4 under 0°, 30°, 45°, 60°, 90°. Divide each by 4, then take the square root — that gives the sin row: 0, 1/2, 1/√2, √3/2, 1. The cos row is the same list reversed, and tan is sin divided by cos. The other three ratios are the reciprocals.
What are sin, cos and tan in a right triangle?
For an angle θ, sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse and tan θ = opposite ÷ adjacent. The memory aid is SOH CAH TOA. The remaining three ratios are reciprocals: cosec θ = 1/sin θ, sec θ = 1/cos θ and cot θ = 1/tan θ.
Why is tan 90 degrees not defined?
Because tan θ = sin θ ÷ cos θ, and at 90° that becomes 1 ÷ 0. Division by zero has no value, so tan 90° is undefined rather than infinite. The same happens to sec 90°, and to cosec 0° and cot 0°, where sin 0° = 0 sits in the denominator.
What is the ASTC rule?
ASTC tells you the sign of each ratio by quadrant, read anticlockwise from the first: All positive, then Sin, then Tan, then Cos, each with its reciprocal. To evaluate any angle, find the acute reference angle to the x-axis, read its value from the 0 to 90 table, then attach the sign. So cos 120° = −cos 60° = −1/2.
What are the main trigonometric identities for Class 10?
The three Pythagorean identities are sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ. You also need the complementary angle rules such as sin(90° − θ) = cos θ and tan(90° − θ) = cot θ. Together these solve almost every proving question in the Class 10 paper.
How do I convert degrees to radians for the unit circle?
Since 180° = π radians, multiply the degrees by π/180. That makes 30° = π/6, 45° = π/4, 60° = π/3, 90° = π/2 and 360° = 2π. The unit circle here shows both the degree and the radian value for every position as you drag the point.
Can I print the trigonometry table?
Yes. Choose the angle range and whether you want exact surds or decimals, add your name if you like, then print the cheat sheet or download it as a PNG image. It prints on a single A4 page with the table, the identities and the ASTC rule together.