CIRCULAR FUNCTIONS
Definition Of Circular Functions
Circular Functions are functions that are defined using a unit circle.
Example of Circular Functions
The functions sine, cosine, tangent, secant, cosecant, and cotangent are examples of circular functions
Video Examples: Circular Functionss
Solved Example onCircular Functions
Ques: State the signs of sin θ and cos θ for values of θ in the given interval (0,
).
Choices:
A. +, -
B. +, +
C. -, -
D. -, +
Correct Answer: B
Solution:
Step 1: Let θ be any angle and P(x, y) be any point on the terminal side of the angle in the interval (0, ).
Step 2: Let r denote the distance from P(x, y) to the origin. Then 
.
Step 3:
Step 4:
. Both are positive, i.e. +, +.
Quick Summary
- Circular functions relate angles to coordinates on the unit circle.
- Sine and cosine are fundamental circular functions; others are derived from them.
- The domain of circular functions is all real numbers (angles), often expressed in radians.
🍎 Teacher Insights
Emphasize the visual connection between angles, the unit circle, and the values of sine and cosine. Use interactive tools to demonstrate how the values of trigonometric functions change as the angle varies.🎓 Prerequisites
- Unit Circle
- Angles in Standard Position
- Basic Trigonometric Ratios (Sine, Cosine, Tangent)
Check Your Knowledge
Q1: In which quadrant are both sin(θ) and cos(θ) positive?
Q2: If the coordinates of a point on the unit circle are (0, -1), what is the value of sin(θ)?
Frequently Asked Questions
Q: What is a unit circle?
A: A circle with a radius of 1, centered at the origin (0,0) of a coordinate plane.
Q: How are sine and cosine defined on the unit circle?
A: For an angle θ, sin(θ) is the y-coordinate and cos(θ) is the x-coordinate of the point where the terminal side of the angle intersects the unit circle.