MAT1510 ASSIGNMENT 4 ANSWERS 2024

MAT1510
ASSIGNMENT 4, 2024
ASSIGNMENT 04
Due date: Monday, 29 July 2024
Total Marks: 100


UNIQUE ASSIGNMENT NUMBER: 151133




MAY 19, 2024
[COMPANY NAME]
[Company address]

, ASSIGNMENT 04


QUESTION 1

(1.1)
(a) P(x,y) = (cos(7π/6), sin(7π/6)) = (-√3/2, -1/2)
(b) P(x,y) = (cos(-5π/6), sin(-5π/6)) = (√3/2, -1/2)
(c) P(x,y) = (cos(8π/3), sin(8π/3)) = (-1/2, √3/2)
(d) P(x,y) = (cos(3π/2), sin(3π/2)) = (0, -1)

(1.2)
(a) t = -7π/6 + (3π/2) = 5π/3
P(x,y) = (cos(5π/3), sin(5π/3)) = (-1/2, √3/2)
(b) t = 7π/6 + π = 19π/6
P(x,y) = (cos(19π/6), sin(19π/6)) = (√3/2, 1/2)
(c) t = 2π - 7π/6 = 5π/6
P(x,y) = (cos(5π/6), sin(5π/6)) = (√3/2, 1/2)
(d) t = 7π/6 - (3π/2) = -π/3
P(x,y) = (cos(-π/3), sin(-π/3)) = (1/2, -√3/2)

(1.3)
(a) Reference angle = 7π/8
(b) Reference angle = π/3
(c) Reference angle = π/2
(d) Reference angle = 5π/6


QUESTION 2

t sin(t −π) cos(t) sin(2π −t) cos(t +π) Smallest positive value of t
7π/4 -√2/2 -√2/2 √2/2 -√2/2 3π/4
QUESTION 3

To find the amplitude, period, and phase shift for each function, we'll
use the general forms of the sine and cosine functions and then sketch
the graph of one complete period.