Questions and Answers
If the sum of the measures of two angles is 180 degrees, the angles are called?
The sine of an acute angle equals the cosine of its complement.
True
What are the three primary trigonometric ratios?
Sine, Cosine, Tangent
In the context of a right-angled triangle, what is the side opposite the right angle called?
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How many quadrants are there in a Cartesian plane?
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The angles of sizes greater than 360 degrees will always lie in any of the four ______.
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What is the basic angle in trigonometry?
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What is the course code for Trigonometry and Coordinate Geometry?
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How many credit units is the MATH103 course worth?
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In which year of study is MATH103 taken?
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What are the two main topics covered in the MATH103 course?
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Trigonometry is relevant only in theoretical mathematics.
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Which of the following are prerequisites for MATH103? (Select all that apply)
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Match the following activities with their descriptions:
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This course involves the study of __________ ratios.
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What is the grading scale range for an 'A' in MATH103?
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The MATH103 course includes field activities.
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What are the most commonly used trigonometric ratios?
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What are inverse trigonometric functions also known as?
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What is the principal value of the inverse sine function denoted by?
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The angles _____, _____, _____, _____, and _____ are commonly used angles.
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The principal value of y for sin(y) gives the angle whose sine is known.
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Which quadrant would the angle for sin(y) be found if sin is positive?
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What do you need to do before finding trigonometric ratios of angles expressed in radians?
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Cosine in the second quadrant is negative.
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What is the relationship of inverse trigonometric functions to their principal values?
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Which of the following angles is NOT one of the common angles?
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Which of the following ratios are positive in the first quadrant?
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Match the following quadrants with their trigonometric ratio signs:
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Find the quadrant of the angle 1000 degrees.
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Determine whether the sine of 150° is positive or negative.
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In the third quadrant, what happens to the sine and cosine?
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What acronym can be used to remember the signs of trigonometric ratios in the quadrants?
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The reciprocal of sine is called _____ and the reciprocal of cosine is called _____.
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What trigonometric ratios are positive in the second quadrant?
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Which of these relationships is true?
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The tangent of an angle between 270° and 360° is positive.
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What is the acronym for remembering the basic trigonometric ratios?
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Study Notes
Course Overview
- Course Code: MATH103
- Title: Trigonometry and Coordinate Geometry
- Credit Units: 2CU
- Level: First-year students in BSc Computer Science
- Duration: 11 weeks with 3 hours of weekly study required
Course Description
- Covers trigonometric ratios, identities, and coordinate geometry.
- Applications include real-life scenarios in science, engineering, and navigation.
- Modules include trigonometric functions, solving triangles, and the general equation of a circle.
Key Components
-
Modules and Study Sessions:
- Two Modules with eight study sessions focusing on trigonometric ratios, equations, and coordinate systems.
- First module emphasizes trigonometric fundamentals while the second module introduces coordinate geometry principles.
Course Prerequisites
- No formal prerequisites but requires:
- Proficiency in English and basic computer skills.
- Knowledge of O level Mathematics.
Learning Resources
- Recommended textbooks include works by Amazigo, David-Osuagwu, and Odili.
- Additional resources for further reading in mathematics.
Course Outcomes
- Ability to define and compute trigonometric ratios and their reciprocals.
- Skills in identifying trigonometric values using tables and graphing functions.
- Understanding of sine and cosine rules for triangles.
- Capability to determine bearings and solve problems related to height and distance.
Activities to Support Learning
- Engaging with courseware, audio, and video materials.
- Participation in discussions and group assignments.
- Field work, optional tutorials, and assessment activities.
Assessment and Grading
- Continuous assessments account for 40% of the final grade including individual tests, group assignments, and quizzes.
- A summative exam (CBT and essay) accounts for 60% of the final grade.
- Grading scale from A (70-100%) to F (0-44%).
Additional Resources
- Links to open educational resources including OER Commons and Academic Earth for supplementary materials.
- Emphasis on using online platforms to enhance learning engagement and access resources.
Academic Calendar Highlights
- Semester starts mid-February with examinations in the first two weeks of January.
- One week break between semesters, with optional third semester for accelerated courses.
Course Structure and Weekly Schedule
- Weekly activities involve reading course materials, viewing instructional videos, and engaging in discussion forums.
- Structured schedule helps students stay organized and manage their study time effectively.### Course Overview
- Focus on Trigonometry and Coordinate Geometry.
- Covers definitions, applications, and relationships of trigonometric ratios, identities, and equations.
- Emphasis on practical problem-solving skills involving angles, distances, and coordinates.
Study Sessions Breakdown
- Week 6: Trigonometric Identities and Equations
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Week 6: Solution of Triangle (Sine and Cosine Values)
- Understanding angles of elevation and depression.
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Week 7 & 8: Bearings
- Navigation concepts using angles and direction.
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Week 9 & 10: Cartesian Coordinate System
- Introduction to plotting points and understanding the plane.
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Week 11 & 12: Coordinate Geometry (Circle)
- Investigate the properties and equations of circles.
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Week 13: Revision/Tutorials
- Review and consolidate knowledge from the semester.
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Weeks 14 & 15: Semester Examination
- Assessment of knowledge acquired throughout the course.
Module 1: Circular Measures
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Study Session 1: Trigonometric Ratios I
- Focus on defining and calculating trigonometric ratios: sine, cosine, tangent.
Key Learning Outcomes
- Ability to define trigonometric ratios and their relationships.
- Identify the boundaries and quadrants for given angles.
- Calculate basic angles and their corresponding trigonometric ratios.
Trigonometric Ratios
- Ratios of sides in a right-angled triangle:
- Sine = Opposite / Hypotenuse
- Cosine = Adjacent / Hypotenuse
- Tangent = Opposite / Adjacent
- Understanding of complementary angles where:
- Sine of an angle equals cosine of its complement.
Trigonometric Ratios of Any Angle
- Extensions from acute angles to all angles using a unit circle.
- Quadrants defined in the Cartesian coordinate system:
- 1st Quadrant: (0^\circ) to (90^\circ) (all positive)
- 2nd Quadrant: (90^\circ) to (180^\circ) (sine positive, cosine negative)
- 3rd Quadrant: (180^\circ) to (270^\circ) (tangent positive)
- 4th Quadrant: (270^\circ) to (360^\circ) (cosine positive, sine negative)
Signs of Trigonometric Ratios in Different Quadrants
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Acronyms for signs:
- CAST: Cosine positive in 4th, All positive in 1st, Sine positive in 2nd, Tangent positive in 3rd.
- ASTC: All positive in 1st, Sine positive in 2nd, Tangent positive in 3rd, Cosine positive in 4th.
Additional Activities
- Tutor-marked assignments for practice on trigonometric equations and identifying quadrants based on angle measures.
- Importance of engaging in self-assessment questions and additional activities to reinforce learning.
Conclusion and Practical Applications
- Essential to understand trigonometric principles for applications in physics, engineering, architecture, and various fields where angles and measurements are critical.### Trigonometric Ratios
- Trigonometric ratios for right-angled triangles are summarized in the acronym SOH CAH TOA.
- Sine (sin): Opposite side / Hypotenuse (SOH)
- Cosine (cos): Adjacent side / Hypotenuse (CAH)
- Tangent (tan): Opposite side / Adjacent side (TOA)
- Inverse relationships exist between trigonometric ratios of an acute angle and its complementary angle.
Trigonometric Ratios for Obtuse Angles
- For obtuse angles, the sine and cosine behave such that:
- Sine: ( \sin(360° - \theta) = - \sin(\theta) )
- Cosine: ( \cos(360° - \theta) = \cos(\theta) )
Relationships of Trigonometric Ratios
- The basic angle is essential for determining the value and sign of trigonometric ratios, depending on which quadrant the angle resides in.
- The six trigonometric functions include sine, cosine, tangent, cosecant, secant, and cotangent.
Reciprocals of Trigonometric Ratios
- Each trigonometric ratio has a reciprocal:
- Cosecant (csc): Reciprocal of sine.
- Secant (sec): Reciprocal of cosine.
- Cotangent (cot): Reciprocal of tangent.
- Quadrant properties dictate whether the ratios are positive or negative:
- 1st Quadrant: All ratios positive.
- 2nd Quadrant: Sine and cosecant positive.
- 3rd Quadrant: Tangent and cotangent positive.
- 4th Quadrant: Cosine and secant positive.
Using Trigonometric Tables
- Trigonometric tables provide values for sine, cosine, and tangent that are used to find their reciprocals.
- Normal angles and their values can be referenced in four-figure tables, which are more efficient than calculating from scratch.
Inverse Trigonometric Functions
- Inverse functions allow finding the angle when the trigonometric value is known.
- Notation and definition for inverse functions are important for solving problems without extensive calculations.
Common Angle Ratios
- Specific trigonometric ratios for basic angles (0°, 30°, 45°, 60°, 90°, 180°, 270°, 360°) should be memorized for efficiency:
- 0°: sin = 0, cos = 1, tan = 0
- 30°: sin = 1/2, cos = √3/2, tan = 1/√3
- 45°: sin = cos = √2/2, tan = 1
- 60°: sin = √3/2, cos = 1/2, tan = √3
- 90°: sin = 1, cos = 0, tan = undefined
Summary and Conclusion
- Understanding trigonometric ratios, their relationships, and their positive/negative quadrant properties is crucial for accurate calculations in trigonometry.
- Mastery of the unit circle and inverse functions enhances problem-solving capabilities in various mathematical contexts.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers key concepts from the MATH103 course on Trigonometry and Coordinate Geometry at Ahmadu Bello University. Students will engage with questions related to angles, triangles, and their respective geometric relationships. Prepare to test your knowledge and understanding of these foundational math principles.
