How to do inverse trig functions on calculator?

To do inverse trig functions on a calculator, enter the value and press either the arcsin, arccos and arctan buttons OR buttons.  The functions arcsin(x), arccos(x) and arctan(x) are the inverse functions of the 3 main trigonometric functions sin(x), cos(x), and tan(x) formed by a reflection across the line y=x. This results in the (x,y) points of sin(x), cos(x) and tan(x) switching their order (y,x) in each inverse

Sine

A function is a rule that assigns exactly one output to each input. In trigonometry there are three main functions sine, cosine, and tangent based on the ratios of sides corresponding to angles within a right triangle. The sine function written as sin(x) has the input of an angle written in degrees or radians and an output as a specific ratio for that angle within a right triangle. The ratio for sine is opposite / hypotenuse. When graphed these inputs form a wavy graph that begins at the origin.

Cosine

The cosine function written as cos(x) has the input of an angle written in degrees or radians and an output as a specific ratio for that angle within a right triangle. The ratio for cosine is adjacent / hypotenuse. When graphed these inputs form a wavy graph that begins at its y-intercept (0,1).

Tangent

The tangent function written as tan(x) has the input of an angle written in degrees or radians and an output as a specific ratio for that angle within a right triangle. The ratio for tangent is opposite / adjacent. When graphed these inputs form a repeating vertical curved graph.

Arcsin

As the arcsin(x) is the inverse of the sin(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arcsin is the triangle side ratios (opposite / hypotenuse) and they align to the angle outputs of this function. For example, if sin (30) = 1/2 then arcsin(1/2) = 30. By pressing the arcsin button on your calculator it reverses the inputs and outputs of the sine graph.

Arccos

As the arccos(x) is the inverse of the cos(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arccos is the triangle side ratios (adjacent / hypotenuse) and they align to the angle outputs of this function. For example, if cos (60) = 1/2 then arccos(1/2) = 60. By pressing the arccos button on your calculator it reverses the inputs and outputs of the cosine graph.

Arctan

As the arctan(x) is the inverse of the tan(x) function, its function is defined as having inputs and outputs which have been reversed. The input of arctan is the triangle side ratios (opposite / adjacent) and they align to the angle outputs of this function. For example, if tan (45) = 1 then arctan(1) = 45. By pressing the arctan button on your calculator it reverses the inputs and outputs of the tangent graph.

Category

Grade: High School - 10/11

Subject: Algebra 2

Chapter: Inverse Trig Functions

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