Principal Values
Principal Values
Principal Values
The set of values that a calculator can output when taking the inverse trigonometric ratio.
The set of values that a calculator can output when taking the inverse trigonometric ratio.
- P = sin-1x, –90° ≤ P ≤ 90°
- P = cos-1x, 0° ≤ P ≤ 180°
- P = tan-1x, –90° < P < 90°
What is so special about these set of values?
What is so special about these set of values?
You can use the Explore! applet below to study the properties of the curve in the given range before checking the answer.
You can use the Explore! applet below to study the properties of the curve in the given range before checking the answer.
- The trigonometric function is 1 : 1 in the given domain. Functions must be 1 : 1 (1 x-value for each y-value and vice-versa) in order for an inverse function to exist.
- The trigonometric function is smooth (differentiable at all points, i.e. no asymptotes for tangent).
Explore!
Explore!
Use the applet below to observe the relationship between the domain and range of the Principal Values with each Trigonometric Function.
Use the applet below to observe the relationship between the domain and range of the Principal Values with each Trigonometric Function.
Summary of Principal Values for all 6 Trigonometric Functions
Summary of Principal Values for all 6 Trigonometric Functions