The arccosine of x is defined as the inverse cosine function of x when -1≤x≤1. (Here cos-1 x means the inverse cosine and does not mean cosine to the power of -1).

Inverse tan is the inverse function of the trigonometric function ‘tangent’. It is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle. Based on this function, the value of tan 1 or arctan 1 or tan 10, etc.

Using the tan-1x convention may lead to confusion about the difference between arctangent and cotangent. It turns out that arctan and cot are really separate things: cot(x) = 1/tan(x) , so cotangent is basically the reciprocal of a tangent, or, in other words, the multiplicative inverse.

arccosine

Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, 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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The domain of the inverse tangent function is (−∞,∞) and the range is (−π2,π2) . The inverse of the tangent function will yield values in the 1st and 4th quadrants. The same process is used to find the inverse functions for the remaining trigonometric functions–cotangent, secant and cosecant. Function. Domain.

If you have a numerical value and you want the size of the angle whose sine has this value, you get something like this, where the value is a number and the arcsin is expressed in degrees of arc. It essentially reverses the process of the sine function. It is called “arcsin” because it gives you a measure of the arc.

The exact value of arcsin(12) arcsin ( 1 2 ) is π6 .

The inverse function of sine. Basic idea: To find sin-1(½), we ask “what angle has sine equal to ½?” The answer is 30°. As a result we say sin-1(½) = 30°. In radians this is sin-1(½) = π/6….index: subject areas.

Therefore, principal value of sin-1(-1/2) = -π/6.

sin−12x will be in {0,1], so that, f(x)=sin−12x∈[0,√π2] . Thus, Domain is [0,12] and, Range is [0,√π2] .