iCoachMath
STEM Excellence Series: Empowering the Next Generation
ARCSINE
Arcsine
Definition Of Arcsine
Arcsine is the inverse function of sine. It is also written as arcsin or sin-1. If y = sin x, then x = arcsin y.
Examples of Arcsine
or 
This means that the angle 300 has sine equal to 
.
Video Examples: Arcsine
Solved Example on Arcsine
Ques: arcsin(0.1218) = ?
Choices:
A. 120
B. 830
C. 780
D. 70
Correct Answer: D
Solution:
Step 1: arcsin(0.1218) = 70, rounded to the nearest degree. [Use calculator in degree mode.]
Quick Summary
- Arcsine returns the angle whose sine is a given number.
- The domain of arcsine is [-1, 1].
- The range of arcsine is [-π/2, π/2] radians or [-90°, 90°] degrees.
\[ x = \arcsin(y) \]
⚠️ Common Mistakes
- Confusing arcsine with cosecant.
- Forgetting to restrict the range of arcsine.
- Using calculator in radian mode when degree mode is needed.
🌍 Real-World Uses
- Calculating the launch angle of a projectile to hit a specific target, given the initial velocity and distance.
- Determining the angle of elevation needed to point a telescope at a star, given the star's declination and the observer's latitude.
- Designing the curvature of a road or railway to safely handle a specific speed, using the angle of banking.
📋 Standards Alignment
CCSS.MATH.HSF.TF.B.6CCSS.MATH.HSF.TF.C.7
🔗 Related Links
🍎 Teacher Insights
Emphasize the restricted range of arcsine to ensure students understand it returns a specific angle within that range.🎓 Prerequisites
- Sine function
- Inverse functions
- Unit circle
Check Your Knowledge
Q1: arcsin(0.5) = ?
Q2: What is arcsin(1)?
Frequently Asked Questions
Q: What is the domain of arcsine?
A: The domain of arcsine is [-1, 1].
Q: What is the range of arcsine?
A: The range of arcsine is [-π/2, π/2] radians or [-90°, 90°] degrees.