Mathematics · 1st secondary · First Term

Trigonometry — Related Angles

About this lesson

This unit covers the relations between trigonometric functions of related angles, specifically angles of the form θ, 180°−θ, 180°+θ, 360°−θ, 90°−θ, 90°+θ, 270°−θ, and 270°+θ. It uses the unit circle and reflections to derive identities such as sin(180°−θ)=sinθ, cos(180°−θ)=−cosθ, etc. It also introduces the general solution of trigonometric equations in the form sinα=cosβ, secα=cscβ, and tanα=cotβ, using complementary angle relationships. Students are expected to find exact values of trigonometric functions for angles beyond 0°–90°, simplify expressions, prove identities, and solve equations for general solutions. The unit includes worked examples, 'Try to solve' exercises, and a set of review questions covering completion, multiple choice, and problem-solving tasks.

Main topics in this lesson

  • Relations between trigonometric functions of related angles
  • General solution of trigonometric equations
  • Complementary and supplementary angle identities
  • Using the unit circle and reflections

Key terms and vocabulary

  • related angles
  • trigonometric functions
  • unit circle
  • reflection
  • standard position
  • complementary angles
  • supplementary angles
  • general solution
  • trigonometric equations

Questions and answers on Trigonometry — Related Angles - practice and revision

Multiple choice questions on this lesson in Mathematics for 1st secondary, First Term, with practice exercises for revision and exam preparation.

1

قيمة cos 90° + θ إذا كان sinθ = 0.6 تساوي:

  • 1 -0.6
  • 2 0.6
  • 3 -0.8
  • 4 0.8
2

قيمة sin 180° + θ إذا كان sinθ = 0.6 تساوي:

  • 1 -0.6
  • 2 0.6
  • 3 -0.8
  • 4 0.8
3

قيمة csc 150° تساوي:

  • 1 2
  • 2 -2
  • 3 1/2
  • 4 -1/2
4

قيمة sec 300° تساوي:

  • 1 2
  • 2 -2
  • 3 √3/2
  • 4 -√3/2
5

إذا كان tanα = cotβ فإن الحل العام للعلاقة هو:

  • 1 α + β = 90°
  • 2 α = β
  • 3 α + β = 180°
  • 4 α − β = 90°
6

إذا كان sinα = cosβ فإن الحل العام للعلاقة هو:

  • 1 α + β = 90° أو α + β = 270°
  • 2 α = β فقط
  • 3 α − β = 90°
  • 4 α + β = 180°

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