MATH103: Trigonometry & Coordinate Geometry
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Questions and Answers

If the sum of the measures of two angles is 180 degrees, the angles are called?

  • Complementary angles
  • Vertical angles
  • Adjacent angles
  • Supplementary angles (correct)

    • 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?

    <p>Hypotenuse</p> Signup and view all the answers

    How many quadrants are there in a Cartesian plane?

    <p>Four</p> Signup and view all the answers

    The angles of sizes greater than 360 degrees will always lie in any of the four ______.

    <p>quadrants</p> Signup and view all the answers

    What is the basic angle in trigonometry?

    <p>The acute angle that is less than 360 degrees.</p> Signup and view all the answers

    What is the course code for Trigonometry and Coordinate Geometry?

    <p>MATH103</p> Signup and view all the answers

    How many credit units is the MATH103 course worth?

    <p>2CU</p> Signup and view all the answers

    In which year of study is MATH103 taken?

    <p>First year</p> Signup and view all the answers

    What are the two main topics covered in the MATH103 course?

    <p>Trigonometry and Coordinate Geometry</p> Signup and view all the answers

    Trigonometry is relevant only in theoretical mathematics.

    <p>False</p> Signup and view all the answers

    Which of the following are prerequisites for MATH103? (Select all that apply)

    <p>Basic Computer Operations proficiency</p> Signup and view all the answers

    Match the following activities with their descriptions:

    <p>Studying courseware = Reading provided materials Listening to course audios = Engaging with audio content for learning Watching relevant course videos = Viewing visual content for course material Field activities = Practical application in real-world settings</p> Signup and view all the answers

    This course involves the study of __________ ratios.

    <p>trigonometric</p> Signup and view all the answers

    What is the grading scale range for an 'A' in MATH103?

    <p>70-100</p> Signup and view all the answers

    The MATH103 course includes field activities.

    <p>True</p> Signup and view all the answers

    What are the most commonly used trigonometric ratios?

    <p>Sine, cosine, and tangent.</p> Signup and view all the answers

    What are inverse trigonometric functions also known as?

    <p>Circular functions.</p> Signup and view all the answers

    What is the principal value of the inverse sine function denoted by?

    <p>sin^(-1) or arcsin.</p> Signup and view all the answers

    The angles _____, _____, _____, _____, and _____ are commonly used angles.

    <p>0°, 30°, 45°, 60°, 90°</p> Signup and view all the answers

    The principal value of y for sin(y) gives the angle whose sine is known.

    <p>True</p> Signup and view all the answers

    Which quadrant would the angle for sin(y) be found if sin is positive?

    <p>1st or 2nd quadrant.</p> Signup and view all the answers

    What do you need to do before finding trigonometric ratios of angles expressed in radians?

    <p>Convert the angles in radians to degrees or vice versa.</p> Signup and view all the answers

    Cosine in the second quadrant is negative.

    <p>True</p> Signup and view all the answers

    What is the relationship of inverse trigonometric functions to their principal values?

    <p>One value is related to an infinite number of values of the function.</p> Signup and view all the answers

    Which of the following angles is NOT one of the common angles?

    <p>120°</p> Signup and view all the answers

    Which of the following ratios are positive in the first quadrant?

    <p>All of the above</p> Signup and view all the answers

    Match the following quadrants with their trigonometric ratio signs:

    <p>1st Quadrant = All positive 2nd Quadrant = Sine positive, Cosine negative, Tangent negative 3rd Quadrant = Tangent positive, Sine negative, Cosine negative 4th Quadrant = Cosine positive, Sine negative, Tangent negative</p> Signup and view all the answers

    Find the quadrant of the angle 1000 degrees.

    <p>2nd quadrant.</p> Signup and view all the answers

    Determine whether the sine of 150° is positive or negative.

    <p>Positive.</p> Signup and view all the answers

    In the third quadrant, what happens to the sine and cosine?

    <p>Sine is negative, Cosine is negative</p> Signup and view all the answers

    What acronym can be used to remember the signs of trigonometric ratios in the quadrants?

    <p>CAST</p> Signup and view all the answers

    The reciprocal of sine is called _____ and the reciprocal of cosine is called _____.

    <p>cosecant, secant</p> Signup and view all the answers

    What trigonometric ratios are positive in the second quadrant?

    <p>Cosecant</p> Signup and view all the answers

    Which of these relationships is true?

    <p>Tangent = Sine / Cosine</p> Signup and view all the answers

    The tangent of an angle between 270° and 360° is positive.

    <p>False</p> Signup and view all the answers

    What is the acronym for remembering the basic trigonometric ratios?

    <p>SOH CAH TOA</p> Signup and view all the answers

    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
    • Week 6: Solution of Triangle (Sine and Cosine Values)
      • Understanding angles of elevation and depression.
    • Week 7 & 8: Bearings
      • Navigation concepts using angles and direction.
    • Week 9 & 10: Cartesian Coordinate System
      • Introduction to plotting points and understanding the plane.
    • Week 11 & 12: Coordinate Geometry (Circle)
      • Investigate the properties and equations of circles.
    • Week 13: Revision/Tutorials
      • Review and consolidate knowledge from the semester.
    • Weeks 14 & 15: Semester Examination
      • Assessment of knowledge acquired throughout the course.

    Module 1: Circular Measures

    • 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

    • 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.

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    MATH103: Trigonometry and Coordinate Geometry PDF

    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.

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