Trigonometry and Analytic Geometry are crucial components of the Registered Electrical Engineers Licensure Examination in the Philippines, encompassing essential mathematical concepts vital for success in the field of electrical engineering. Trigonometry, with its focus on angles and triangles, plays a significant role in solving complex problems involving electrical circuits, waveforms, and signal processing. Understanding trigonometric functions, identities, and relationships is essential for analyzing alternating current circuits, antenna design, and signal modulation.
On the other hand, Analytic Geometry provides the tools to represent geometric shapes and equations algebraically, enabling engineers to model and analyze various electrical systems and components. Mastery of concepts such as lines, circles, parabolas, ellipses, and hyperbolas is crucial for interpreting graphs, plotting coordinates, and solving geometric problems encountered in electrical engineering applications.
In this course tailored for the Registered Electrical Engineers Licensure Examination, students will delve deep into Trigonometry and Analytic Geometry, acquiring the knowledge and skills necessary to excel in their examination and embark on a successful career in the field of electrical engineering.
Electrical Engineers - Trigonometry and Analytic Geometry PRACTICE REVIEWER
Welcome to our Electrical Engineers - Trigonometry and Analytic Geometry Practice Examination! In this session, you'll have the opportunity to test your understanding of key concepts in Trigonometry and Analytic Geometry. The quiz consists of multiple-choice questions covering various topics. Pay close attention to each question and select the best answer. After completing the exam, check the video below for the answer key and explanations.
Trigonometry
1. What is the value of sin(Ï€/4)?
A) √2/2
B) 1
C) √3/2
D) 1/2
2. If cos(θ) = 3/5 and θ is an acute angle, what is the value of sin(θ)?
A) 4/5
B) √7/5
C) 3/4
D) √7/4
3. What is the period of the function f(x) = 2sin(3x)?
A) π
B) 2Ï€
C) 2Ï€/3
D) π/3
4. If tan(α) = -√3 and α is in quadrant III, what is the value of sin(α)?
A) -1/2
B) -√3/2
C) 1/2
D) √3/2
5. What is the value of cot(Ï€/3)?
A) 1
B) √3
C) 1/√3
D) √3/3
6. If sin(β) = 4/5 and β is in quadrant II, what is the value of cos(β)?
A) -3/5
B) -4/5
C) -√7/5
D) -√7/4
7. What is the value of sec(Ï€/6)?
A) 2
B) √3
C) 1/2
D) 2√3
8. If cos(θ) = 1/3 and θ is in quadrant I, what is the value of tan(θ)?
A) √2/3
B) 1/√2
C) √2
D) 1/√3
9. What is the value of sin(5Ï€/3)?
A) -√3/2
B) √3/2
C) -1/2
D) 1/2
10. If cos(α) = -4/5 and α is in quadrant IV, what is the value of csc(α)?
A) -5/4
B) 5/4
C) -5/3
D) 5/3
Analytic Geometry
11. Which of the following equations represents a circle centered at (2, -3) with a radius of 5?
A) (x - 2)^2 + (y + 3)^2 = 5
B) (x - 2)^2 + (y + 3)^2 = 25
C) (x + 2)^2 + (y - 3)^2 = 5
D) (x + 2)^2 + (y - 3)^2 = 25
12. What is the slope of the line passing through the points (-3, 4) and (5, -2)?
A) -1
B) -2/3
C) 2/3
D) 1
13. Which of the following represents a vertical line?
A) y = 2x + 3
B) x = 3
C) y = -3
D) x = -2
14. What is the distance between the points (-1, 2) and (3, -4)?
A) √40
B) 5
C) √20
D) 6
15. Which of the following equations represents a parabola with a vertex at (2, -1) opening upward?
A) y = (x - 2)^2 - 1
B) y = -(x - 2)^2 - 1
C) x = (y + 1)^2 - 2
D) x = -(y + 1)^2 - 2
16. What is the equation of the line parallel to the line 2x - 3y = 6 and passing through the point (4, -1)?
A) 2x - 3y = -14
B) 2x - 3y = 5
C) 2x - 3y = -5
D) 2x - 3y = 14
17. What is the equation of the line perpendicular to the line 3x + 4y = 8 and passing through the point (-2, 1)?
A) 4x - 3y = 10
B) 3x - 4y = -14
C) 4x + 3y = 10
D) 3x - 4y = 14
18. Which of the following represents a hyperbola centered at (0, 0) with vertices at (±3, 0) and asymptotes y = ±(2/3)x?
A) x^2/9 - y^2/4 = 1
B) x^2/4 - y^2/9 = 1
C) x^2/9 - y^2/4 = -1
D) x^2/4 - y^2/9 = -1
19. What are the coordinates of the midpoint of the line segment joining the points (2, 5) and (-4, 1)?
A) (-1, 3)
B) (-2, 3)
C) (0, 6)
D) (-1, 6)
20. What is the equation of the ellipse with foci at (±5, 0) and major axis length of 10?
A) (x/5)^2 + y^2 = 1
B) (x/10)^2 + y^2 = 1
C) x^2 + (y/5)^2 = 1
D) x^2 + (y/10)^2 = 1
WATCH THE VIDEO FOR THE ANSWER KEY AND EXPLANATION
Congratulations on completing the Electrical Engineers - Trigonometry and Analytic Geometry Exam! Stay tuned for more practice online reviewer and educational content to further enhance your understanding of various learning areas.
