Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4] and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

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Therefore, sec(arctan(x)) sec (arctan (x)) is √1+x2 1 + x 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles.

Feb 24, 2025 · Inverse trigonometric functions, also called arc functions, reverse the operations of the basic six trigonometric functions – sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot).

The functions are usually abbreviated: arcsine (arcsin), arccosine (arccos), arctangent (arctan) arccosecant (arccsc), arcsecant (arcsec), and arccotangent (arccot). According to the standard notation for inverse functions (f -1), you will also often see these written as sin -1, cos -1, tan -1 arccsc -1, arcsec -1, and arccot -1.

In a right triangle, the secant of an angle is the length of the hypotenuse divided by the length of the adjacent side. In a formula, it is abbreviated to just 'sec'. Of the six possible trigonometric functions, secant, cotangent, and cosecant, are rarely used.

What is sec (arctan (x)) ?

The three theorems for the intercepted arcs to the angle of two tangents, two secants or 1 tangent and 1 secant are summarized by the pictures below. If you look at each theorem, you really only need to remember ONE formula.

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because secant is negative in the second quadrant. The exact value of sec(0) sec (0) is 1 1. Multiply −1 - 1 by 1 1. The exact value of arctan(−1) arctan (- 1) is − π 4 - π 4. The result can be shown in multiple forms.