A tangent to a circle is a straight line which touches the circle at only one point. This point is called the point of tangency. The tangent to a circle is perpendicular to the radius at the point of tangency.

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.

The tangent line is useful because it allows us to find the slope of a curved function at a particular point on the curve. We learned a long, long time ago in a math class far, far away that we could find the slope of a line, but we’ve never learned how to find the slope of a curved function.

So, the inverse of a tangent is called the arctangent (or arctan for short). Think of the arctangent as a tool you can use like any other inverse operation when solving a problem.

Two keys on the calculator toggle the other keys:

1. 2nd: Tap to change trigonomic (sin, cos, tan) and hyperbolic functions to the inverse. The button is outlined in black when active.
2. Rad/Deg: Tap to switch between Radians and Degrees for trigonomic functions.

If you need a calculator that has a back button, head to the App Store and install Calculator with History +. Not only is this app absolutely free, but it will also show you your calculation history.

sine function

Domain and range: The domain of the arcsine function is from −1 to +1 inclusive and the range is from −π/2 to π/2 radians inclusive (or from −90° to 90°). The arcsine function can be extended to the complex numbers, in which case the domain is all complex numbers.

arcsin is defined to be the inverse of sin but restricted to a certain range. Hence arcsin(sin(x))=x if x is within this range (generally either 0 to 2π or −π to π) or a value y such that sin(y)=sin(x) i.e. y=x+2πn or y=π−x+2πm for some n∈Z or m∈Z and y is in this range.

So, sin (-30°) = -1/2. So, we could say arcsin (-1/2)= -30°.

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