Enter an angle to compute sin(180-A), cos(180-A), and tan(180-A) identities
Angle A (degrees)
Result
Supplementary: 180 - A =
sin(180-A) = sinA
-
cos(180-A) = -cosA
-
tan(180-A) = -tanA
-
Detailed Derivation
Supplementary Angle Identities
sin(180 - A) = sinA
cos(180 - A) = -cosA
tan(180 - A) = -tanA
180 - A is the supplement of A
Supplementary angle identities show how trig functions change when an angle is subtracted from 180 degrees. Sine preserves its value, while cosine and tangent flip signs. This is due to the y-axis reflection on the unit circle.
⚠Supplementary identities work for any angle A. The key difference from complementary identities: sin(90-A) swaps functions, while sin(180-A) changes sign for cos and tan.
What Are Supplementary Angle Identities?
Supplementary angle identities relate trigonometric functions of supplementary angles (angles summing to 180 degrees). They are essential for working with angles greater than 90 degrees and solving trigonometric equations.
Sine Preserved
sin(180-A) = sinA. Sine values are the same for supplementary angles. This is seen in the symmetric sine graph around 90.
Cosine Flips
cos(180-A) = -cosA. Cosine changes sign because the x-coordinate on the unit circle flips across the y-axis.
Tangent Flips
tan(180-A) = -tanA. Since tan = sin/cos, and sin stays while cos flips, tan also flips sign.
Unit Circle View
Point at angle A: (cosA, sinA). Point at 180-A: (-cosA, sinA). The y-coordinate matches, x-coordinate is opposite.
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