Trigonometric Values Table

How the Unit Circle Explains Trigonometric Values

On the unit circle, an angle θ identifies a point whose coordinates are (cos θ, sin θ). The tangent is the ratio sin θ / cos θ whenever cos θ is nonzero. The remaining functions are reciprocals: secant is 1/cos θ, cosecant is 1/sin θ, and cotangent is cos θ/sin θ.

Trigonometric Values in Degrees and Radians

Degrees measure a complete revolution as 360°, while radians measure the same revolution as 2π. To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. Common angles such as 30°, 45°, 60°, and 90° correspond to π/6, π/4, π/3, and π/2 radians.

How to Read the Trigonometric Table

Find the angle in the first column, then read across to the required function. Use exact values when a problem asks for radicals or fractions. Use decimal approximations when a numerical answer is appropriate. Always check whether the function is defined at the selected angle.

Trigonometric Signs by Quadrant

Quadrant I: all six functions are positive. Quadrant II: sine and cosecant are positive; the others are negative. Quadrant III: tangent and cotangent are positive; the others are negative. Quadrant IV: cosine and secant are positive; the others are negative.

Angles on axes are not inside any quadrant. Some reciprocal functions are undefined there because their denominators are zero.

Exact Values vs. Decimal Approximations

Exact trigonometric values preserve mathematical relationships. For example, sin 45° is exactly √2/2, while 0.707107 is a rounded approximation. When solving algebraic or trigonometric expressions, exact values avoid rounding errors that can accumulate across several steps.

Numerical results use JavaScript double precision and are displayed to six decimal places. A very small nonzero value can round to zero; this does not make its reciprocal undefined. The lookup accepts angles within ±1,000,000,000 degrees. Numeric radians or expressions such as pi/3 are supported.