Trigonometric Inverse

• When you use a calculator to take the trigonometric inverse to find an angle, it returns just one value, the principle value.

• Between 0⁰ and 360⁰ there are two angles which will give the same value for the sine, cosine, or tangent.
  
  
• Which angle is the correct angle depends upon the details of the problem you are solving, i.e. you can not always assume that the value your calculator returns is the correct angle.

• Note that there are actually an infinite number of solutions of any trigonometric inverse if you do not limit you answers to be between 0 and 360 degrees.

• It is common practice to state angle between 180^o and 360^o as a negative angle between 0^o and -180^o. For example 270⁰ could be expressed as -90^o.

Inverse Sine
Your calculator returns a value

If then

• If you are trying to find the angle of a vector in the II or III quardrants, you will need to use the alternate solution π - sin^-1(x).

Inverse Cosine
Your calculator returns a value

If then

• If you are trying to find the angle of a vector in the III or IV quardrants, you will need to use the alternate solution π ± cos^-1(x).

Inverse Tangent
Your calculator returns a value

If then

• If you are trying to find the angle of a vector in the II or III quardrants, you will need to use the alternate solution π + tan^-1(x).