MATH 1201-01 – College Algebra – AY2026-T5 Unit 7 Learning Journal Assignment
Activity Unit 7 | Verified study complete Solutions | A+ Graded | 2026 Updates |
100% correct
Department of Mathematics - University of People
MATH 1201 -01 – College Algebra – AY2026-T5
Prof. Pramila Bajpai (Instructor)
Assignment Title: Solving Trigonometric functions and Equations
Introduction
This assignment explores both basic and advanced topics in trigonometry, focusing
on double angle identities, trigonometric equations, and their geometric applications.
Through four organised tasks, we will tackle problems related to right-angled triangles,
factor and solve trigonometric expressions, graph functions, and convert identities into
forms that involve specific trigonometric ratios. These activities aim to enhance both
algebraic skills and conceptual comprehension while emphasizing the interrelated aspects of
trigonometric functions in mathematical analysis. The concepts and identities used in this
assignment are sourced from reputable materials, including Blitzer (2017), OpenStax (2022),
and Yoshiwara (2023).
Task 1
(a) Calculate tan (2θ):
, Given:
• AB = 8 (opposite to θ)
• BC = 6 (adjacent to θ)
• AC = √(8² + 6²) = √(64 + 36) = √100 = 10 (hypotenuse)
Using the formula:
Step 1: tan (θ) = opposite / adjacent = = 1.333
Step 2: Apply the double angle identity: tan (2θ) = (2 × tan (θ)) / (1 - tan² (θ)) (OpenStax,
2022; Yoshiwara, 2023).
Step 3: Substitute tan (θ) = 1.333 into the formula:
• tan (2θ) = (2 × 1.333) / (1 - (1.333) ^2)
Step 4: Evaluate the numerator and denominator:
• Numerator = 2 × 1.333 = 2.666
• Denominator = 1 - (1.333) ^2 = 1 - 1.776889 = -0.776889
Step 5:
• We will then divide the numerator by the denominator:
• tan (2θ) = 2.666 / -0.776889 ≈ -3.429
Activity Unit 7 | Verified study complete Solutions | A+ Graded | 2026 Updates |
100% correct
Department of Mathematics - University of People
MATH 1201 -01 – College Algebra – AY2026-T5
Prof. Pramila Bajpai (Instructor)
Assignment Title: Solving Trigonometric functions and Equations
Introduction
This assignment explores both basic and advanced topics in trigonometry, focusing
on double angle identities, trigonometric equations, and their geometric applications.
Through four organised tasks, we will tackle problems related to right-angled triangles,
factor and solve trigonometric expressions, graph functions, and convert identities into
forms that involve specific trigonometric ratios. These activities aim to enhance both
algebraic skills and conceptual comprehension while emphasizing the interrelated aspects of
trigonometric functions in mathematical analysis. The concepts and identities used in this
assignment are sourced from reputable materials, including Blitzer (2017), OpenStax (2022),
and Yoshiwara (2023).
Task 1
(a) Calculate tan (2θ):
, Given:
• AB = 8 (opposite to θ)
• BC = 6 (adjacent to θ)
• AC = √(8² + 6²) = √(64 + 36) = √100 = 10 (hypotenuse)
Using the formula:
Step 1: tan (θ) = opposite / adjacent = = 1.333
Step 2: Apply the double angle identity: tan (2θ) = (2 × tan (θ)) / (1 - tan² (θ)) (OpenStax,
2022; Yoshiwara, 2023).
Step 3: Substitute tan (θ) = 1.333 into the formula:
• tan (2θ) = (2 × 1.333) / (1 - (1.333) ^2)
Step 4: Evaluate the numerator and denominator:
• Numerator = 2 × 1.333 = 2.666
• Denominator = 1 - (1.333) ^2 = 1 - 1.776889 = -0.776889
Step 5:
• We will then divide the numerator by the denominator:
• tan (2θ) = 2.666 / -0.776889 ≈ -3.429
