Signs of the Trigonometric functions

                          Signs of the Trigonometric functions



The signs of trigonometric functions depend on the quadrant in which the angle lies. Here's a summary of the signs of trigonometric functions in each quadrant:

  1. Quadrant I:

    • All trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are positive.

  2. Quadrant II:

    • Sine (sin⁡) is positive.
    • Cosine (cos⁡) is negative.
    • Tangent (tan⁡) is positive.
    • Cosecant (csc⁡) is positive.
    • Secant (sec⁡) is negative.
    • Cotangent (cot⁡) is positive.

  3. Quadrant III:

    • Sine (sin⁡) is negative.
    • Cosine (cos⁡) is negative.
    • Tangent (tan⁡) is positive.
    • Cosecant (csc⁡) is negative.
    • Secant (sec⁡) is negative.
    • Cotangent (cot⁡) is positive.

  4. Quadrant IV:

    • Sine (sin⁡) is negative.
    • Cosine (cos⁡) is positive.
    • Tangent (tan⁡) is negative.
    • Cosecant (csc⁡) is negative.
    • Secant (sec⁡) is positive.
    • Cotangent (cot⁡) is negative.

Remember the mnemonic

"All Students Take Calculus" (or "All Silver Tea Cups" or "All Smart Tigers Can"), where the first letter of each word corresponds to the sign of the trigonometric functions in each quadrant:

A for All (positive), S for Sine, T for Tangent, C for Cosine (negative).

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