MAT1510 Assignment 04 (751721) Due 16 July 2025

MAT1510
Assignment 04
Unique No: 751721
Due 16 July 2025

,MAT1510

Assignment 04

UNIQUE No: 751721

Due Date: Wednesday,16 July2025



Accurate Solution & Well Labeled Diagrams


Question 1: 36 Marks

(1.1) Find the terminal points P( x,y) on the unit circle determined by the given value t

(3 marks)

(3 marks)

(3 marks)

(3 marks)

(1.2) Suppose is the terminal point on the unit circle determined by t. Find the
terminal point determined by each of the following

(3 marks)

(b) t+ π(3 marks)

(c) 2 π− t(3 marks)

(d) (3 marks)

(1.3) Find the reference number t̄for each of the following values of t

(3 marks)

(3 marks)



(3 marks)

,Problem 1.1: Terminal Points on the Unit Circle

The unit circle is defined by points ( x,y) where x= cos t, y= sin t, and tis the angle in
radians from the positive x-axis. We need to find the coordinates for each given t.




Problem Statement: Find the terminal point P( x,y) on the unit circle for

.

Step 1: Determine the angle’s position.

A negative angle indicates clockwise rotation. The angle is equivalent to rotating
radians clockwise. Since 2 πis one full revolution, compute the equivalent positive angle:


.
The angle ) lies in the second quadrant.

Step 2: Find the reference angle.

In the second quadrant, the reference angle t̄is:


.
Step 3: Compute coordinates using the reference angle.

For , the coordinates are . In the second quadrant, cosine is
negative, sine is positive:


.

Final Answer: The terminal point is .

, Problem Statement: Find the terminal point P( x,y) on the unit circle for

.

Step 1: Reduce the angle modulo 2 π.

Since , compute:


.
Subtract 2 π:


.
The angle is in the second quadrant.

Step 2: Use the reference angle.

Reference angle: .

Coordinates: .

Final Answer: The terminal point is .