iCoachMath
STEM Excellence Series: Empowering the Next Generation
ARCCOSINE
Arccosine
Ques:
Definition Of Arccosine
Arccosine is the inverse function of cosine. It is also written as arccos or cos-1.
If y = cos x, then x = arccos y.
Examples of Arccosine
or 
This means that the angle 300 has cosine equal to 
.
Video Examples: Arccos Tnverse Trig Function
Solved Example Clockple on Approximate
Ques: 
Choices:
A. 0.3
B. 0.2
C. 0.5
D. 0.6
Correct Answer: D
Solution:
Step 1: Recall that cos(arccos x) = x, for - 1 ≤ x ≤ 1.
Quick Summary
- Arccosine is the inverse of cosine.
- It finds the angle whose cosine is a given number.
- The domain of arccosine is [-1, 1].
- The range of arccosine is [0, π] (in radians) or [0, 180] (in degrees).
\[ arccos(y) = x iff cos(x) = y, where -1 ≤ y ≤ 1 and 0 ≤ x ≤ π \]
🍎 Teacher Insights
Emphasize the restricted range of arccosine. Use the unit circle to visualize arccosine values for common angles. Relate arccosine to right triangles when discussing trigonometric ratios.🎓 Prerequisites
- Cosine function
- Unit circle
- Inverse functions
Check Your Knowledge
Q1: What is arccos(√3/2)?
Q2: What is the domain of arccos(x)?
Q3: What is the range of arccos(x)?
Frequently Asked Questions
Q: What is the arccosine of 1?
A: The arccosine of 1 is 0 because cos(0) = 1.
Q: What is the arccosine of 0?
A: The arccosine of 0 is π/2 (or 90 degrees) because cos(π/2) = 0.
Q: What is the domain of arccosine?
A: The domain of arccosine is [-1, 1].