MATH 1201 Assignment Unit 7 |
Trigonometric Identities, Double-Angle
Formulas & Trigonometric Equations |
2026/2027 Updated | University of the People
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
48 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
This exam assesses mastery of trigonometric identities, double-angle and half-angle formulas, sum and
difference formulas, product-to-sum and sum-to-product transformations, and the solution of trigonometric
equations. Items require multi-step symbolic manipulation, quadrant/sign analysis, general-solution reasoning,
and synthesis across identities and inverse functions, aligned with the 2026/2027 MATH 1201 syllabus.
STUDY GUIDE
Recommended duration: 3 hours. Passing target: 70% (C) for course credit; A+ designation requires 97%.
HIGHP - Page 1 of 15
, 1. If cos = 5/13 and lies in Quadrant III, what is the exact value of sin(2)?
[ ] A. 120/169
[ ] B. 120/169
[ ] C. 60/169
[ ] D. 60/169
CORRECT: A. 120/169
In Quadrant III, sin = 12/13 (since sin² = 1 25/169 = 144/169). Then sin(2) = 2 sin cos = 2(12/13)(5/13) =
120/169. The double-negative yields positive 120/169; 120/169 and ±60/169 arise from sign or factor errors.
2. Which expression is equivalent to (1 cos 2x)/(1 + cos 2x) for all x where it is defined?
[ ] A. tan²x
[ ] B. cot²x
[ ] C. sin²x
[ ] D. cos²x
CORRECT: A. tan²x
Using 1 cos 2x = 2 sin²x and 1 + cos 2x = 2 cos²x, the quotient reduces to sin²x/cos²x = tan²x. cot²x is the
reciprocal, and sin²x or cos²x alone ignores the division.
3. The exact value of cos 75° is:
[ ] A. (6 2)/4
[ ] B. (6 + 2)/4
[ ] C. (2 6)/4
[ ] D. (3 + 1)/4
CORRECT: A. (6 2)/4
cos 75° = cos(45° + 30°) = cos45°cos30° sin45°sin30° = (2/2)(3/2) (2/2)(1/2) = (6 2)/4. Option B is cos 15°,
C is its negative, and D is not a standard exact form.
4. Given cos = 3/5 with in Quadrant IV, find the exact value of sin(/2).
[ ] A. 5/5
[ ] B. 5/5
[ ] C. 25/5
[ ] D. 25/5
CORRECT: A. 5/5
With in Quadrant IV, /2 lies in Quadrant II, so sin(/2) > 0? Correction: /2 (135°, 180°) actually gives positive
sine; however using sin(/2) = ±((1 cos )/2) = ±((1 3/5)/2) = ±(1/5) = ±5/5. Since (270°, 360°), /2 (135°,
HIGHP - Page 2 of 15
Trigonometric Identities, Double-Angle
Formulas & Trigonometric Equations |
2026/2027 Updated | University of the People
Practice Question Bank & Answer Rationale
THIS PACK CONTAINS
48 exam-style multiple-choice questions. Each question includes the correct answer and a complete rationale
for focused revision.
COVERAGE
This exam assesses mastery of trigonometric identities, double-angle and half-angle formulas, sum and
difference formulas, product-to-sum and sum-to-product transformations, and the solution of trigonometric
equations. Items require multi-step symbolic manipulation, quadrant/sign analysis, general-solution reasoning,
and synthesis across identities and inverse functions, aligned with the 2026/2027 MATH 1201 syllabus.
STUDY GUIDE
Recommended duration: 3 hours. Passing target: 70% (C) for course credit; A+ designation requires 97%.
HIGHP - Page 1 of 15
, 1. If cos = 5/13 and lies in Quadrant III, what is the exact value of sin(2)?
[ ] A. 120/169
[ ] B. 120/169
[ ] C. 60/169
[ ] D. 60/169
CORRECT: A. 120/169
In Quadrant III, sin = 12/13 (since sin² = 1 25/169 = 144/169). Then sin(2) = 2 sin cos = 2(12/13)(5/13) =
120/169. The double-negative yields positive 120/169; 120/169 and ±60/169 arise from sign or factor errors.
2. Which expression is equivalent to (1 cos 2x)/(1 + cos 2x) for all x where it is defined?
[ ] A. tan²x
[ ] B. cot²x
[ ] C. sin²x
[ ] D. cos²x
CORRECT: A. tan²x
Using 1 cos 2x = 2 sin²x and 1 + cos 2x = 2 cos²x, the quotient reduces to sin²x/cos²x = tan²x. cot²x is the
reciprocal, and sin²x or cos²x alone ignores the division.
3. The exact value of cos 75° is:
[ ] A. (6 2)/4
[ ] B. (6 + 2)/4
[ ] C. (2 6)/4
[ ] D. (3 + 1)/4
CORRECT: A. (6 2)/4
cos 75° = cos(45° + 30°) = cos45°cos30° sin45°sin30° = (2/2)(3/2) (2/2)(1/2) = (6 2)/4. Option B is cos 15°,
C is its negative, and D is not a standard exact form.
4. Given cos = 3/5 with in Quadrant IV, find the exact value of sin(/2).
[ ] A. 5/5
[ ] B. 5/5
[ ] C. 25/5
[ ] D. 25/5
CORRECT: A. 5/5
With in Quadrant IV, /2 lies in Quadrant II, so sin(/2) > 0? Correction: /2 (135°, 180°) actually gives positive
sine; however using sin(/2) = ±((1 cos )/2) = ±((1 3/5)/2) = ±(1/5) = ±5/5. Since (270°, 360°), /2 (135°,
HIGHP - Page 2 of 15
