1
MATH 1201-01- College Algebra – AY2026-T5 Unit 6 Journal Learning |
Actual study complete solutions | A+ Graded | 2026 Updates | 100%
correct
Solutions to Trigonometric Functions Assignment
Overview
This assignment focuses on fundamental concepts related to trigonometric functions and their
applications in real-life scenarios. These functions effectively model periodic phenomena observable in nature,
including the orbits of celestial bodies, sound wave patterns, and seasonal changes. The objective of this task is
to develop a solid understanding of the unit circle, trigonometric ratios, reference angles, and the examination
of geometric situations involving angles of elevation. It will employ analytical skills and mathematical
techniques through accurate trigonometric formulas and logical analysis (OpenStax, 2022).
Task 1:
A point on the unit circle with given coordinates is provided. From this information, we need to:
• Compute all six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) along
with the formulas used
• Identify the quadrant in which the point is situated and provide a rationale for this identification.
• Calculate both the reference angle and the actual angle formed with the positive x-axis.
(i) Calculation of all 6 trigonometric functions:
, 2
Given coordinates: (x, y) = (-√3/2, 1/2)
r = √(x² + y²) = √ ((-√3/2)² + (1/2)²) = √ (3/4 + 1/4) = √1 = 1
sinθ = y/r = ½
cosθ = x/r = -√3/2
tanθ = y/x = (1/2)/
(-√3/2) = -1/√3 = -
√3/3
cscθ = 1/sinθ = 1/ (1/2) = 2
secθ = 1/cosθ = 1/ (-√3/2) = -2/√3 = -2√3/3
cotθ = 1/tanθ = -√3
(ii) Quadrant Identification:
So, since x = -√3/2 < 0 and y = 1/2 > 0 → the point is located in Quadrant II, which is defined by a negative
xcoordinate and a positive y-coordinate (Abramson, 2023).
(iii) Reference Angle Calculation:
The reference angle is determined as follows:
MATH 1201-01- College Algebra – AY2026-T5 Unit 6 Journal Learning |
Actual study complete solutions | A+ Graded | 2026 Updates | 100%
correct
Solutions to Trigonometric Functions Assignment
Overview
This assignment focuses on fundamental concepts related to trigonometric functions and their
applications in real-life scenarios. These functions effectively model periodic phenomena observable in nature,
including the orbits of celestial bodies, sound wave patterns, and seasonal changes. The objective of this task is
to develop a solid understanding of the unit circle, trigonometric ratios, reference angles, and the examination
of geometric situations involving angles of elevation. It will employ analytical skills and mathematical
techniques through accurate trigonometric formulas and logical analysis (OpenStax, 2022).
Task 1:
A point on the unit circle with given coordinates is provided. From this information, we need to:
• Compute all six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) along
with the formulas used
• Identify the quadrant in which the point is situated and provide a rationale for this identification.
• Calculate both the reference angle and the actual angle formed with the positive x-axis.
(i) Calculation of all 6 trigonometric functions:
, 2
Given coordinates: (x, y) = (-√3/2, 1/2)
r = √(x² + y²) = √ ((-√3/2)² + (1/2)²) = √ (3/4 + 1/4) = √1 = 1
sinθ = y/r = ½
cosθ = x/r = -√3/2
tanθ = y/x = (1/2)/
(-√3/2) = -1/√3 = -
√3/3
cscθ = 1/sinθ = 1/ (1/2) = 2
secθ = 1/cosθ = 1/ (-√3/2) = -2/√3 = -2√3/3
cotθ = 1/tanθ = -√3
(ii) Quadrant Identification:
So, since x = -√3/2 < 0 and y = 1/2 > 0 → the point is located in Quadrant II, which is defined by a negative
xcoordinate and a positive y-coordinate (Abramson, 2023).
(iii) Reference Angle Calculation:
The reference angle is determined as follows:
