The secant modulus is the total stress or strain on an object as described by a stress-strain graph. The tangent modulus is the marginal strain.
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This question probably is referring to a 2% secant modulus, which can be the tensile, flexural or compressive modulus (slope of a stress/strain curve) of a material that is determined from calculating the slope of a line drawn from the origin to 2% strain on a stress/Strain curve.
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The tangent secant angle is the angle between the tangent to a circle and the secant, when the latter is extended.
Secant is a trignometric function. In a right triangle, the secant of an angle is the hypotenuse over the adjacent side. It is also the inverse of cosine. For example secant(x) = 1/cos(x)