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Cofunctions are pairs of trig functions (sine & cosine, tangent & cotangent, secant & cosecant) that are equal at complementary angles — two angles that add up to 90°. This calculator applies the complementary-angle identity, e.g. sin(θ) = cos(90° − θ), to find the matching cofunction value instantly. The idea traces directly back to a right triangle: the two non-right angles in any right triangle always sum to 90°, and the side that's "opposite" one of those angles is simultaneously "adjacent" to the other — which is exactly why sine of one angle equals cosine of its complement.
How it works
Choose a trig function (sin, cos, tan, cot, sec, or csc) and an angle θ. The calculator identifies that function's cofunction partner (sine pairs with cosine, tangent with cotangent, secant with cosecant), computes the complementary angle (90° − θ), and evaluates the partner function at that complementary angle — which, by the identity, always equals your original function's value at θ. The prefix "co-" in cosine, cotangent, and cosecant literally stands for "complement," a naming convention that directly encodes this relationship.
- Enter trig function.
- Enter angle (θ).
- Enter angle unit.
- Click Calculate to see your results.
Examples
sin(30°) and its cofunction
sin(30°) = 0.5, and cos(90° − 30°) = cos(60°) also equals 0.5 — confirming sin(30°) = cos(60°).
tan(20°) and its cofunction
tan(20°) ≈ 0.3640, and cot(90° − 20°) = cot(70°) ≈ 0.3640 as well, since cot(70°) = 1/tan(70°) = 1/2.7475 ≈ 0.3640.
sec(80°) and its cofunction
sec(80°) = 1/cos(80°) ≈ 5.7588, and csc(90° − 80°) = csc(10°) = 1/sin(10°) ≈ 5.7588 — matching, since 80° and 10° are complementary.
Who should use it
- Verifying a value found via a different trig identity.
- Understanding why cosine, cotangent, and cosecant are named the way they are.
- Trigonometry coursework on complementary angles.
Industry applications
- Trigonometry education
- Surveying and navigation (complementary angle problems)
Advantages
- Clarifies the practical meaning behind the "co-" prefix in trig function names.
- Instant, exact verification of the complementary relationship.
Limitations
- Only covers the three standard cofunction pairs — not a general identity solver.
Common mistakes to avoid
- Assuming any two functions are cofunctions — only the three specific pairs (sin/cos, tan/cot, sec/csc) apply.
- Confusing a cofunction pair (related by complementary angles) with a reciprocal pair (like sine and cosecant, which are related by division, not complementary angles).
- Forgetting to subtract from 90° (or π/2 in radians) and instead using the wrong complementary angle.
Best practices
- Use the cofunction identity as a quick way to find an unfamiliar trig value from an equivalent one you already know or can look up.
- Remember the "co-" naming pattern (cosine, cotangent, cosecant) as a memory aid for which functions pair together.
- Double check whether your target angle is in degrees or radians before subtracting from 90° or π/2.
Tips
- Need to solve for all six ratios from just one known value? Use the Trig Identities Calculator.