Mathematics · 1st secondary · First Term

Trigonometry — Finding the Measure of an Angle in Terms of One of its Trigonometric Ratios

About this lesson

This unit teaches students how to find the measure of an angle when given a trigonometric function value, within the range 0° to 360°. It explains the use of inverse trigonometric functions (like sin⁻¹, cos⁻¹, tan⁻¹) and how to determine possible angles in different quadrants based on the sign of the function. Worked examples show using a calculator to find acute reference angles and then adjusting for the correct quadrant. Practice problems involve finding angles from given sine, cosine, tangent, cosecant, secant, and cotangent values, as well as applying these skills to real-world contexts like a ski game ramp, a car ramp, and a ladder against a wall. By the end, students should be able to calculate angle measures in degrees (and sometimes radians) from trigonometric values, identify all possible angles in 0°–360°, and solve simple geometric problems involving right triangles.

Main topics in this lesson

  • Finding angle measures from trigonometric functions
  • Using inverse trigonometric functions
  • Quadrant analysis for angle determination
  • Real-world applications (ski ramp, car ramp, ladder)
  • Unit circle and trigonometric function values

Key terms and vocabulary

  • inverse trigonometric function
  • quadrant
  • acute angle
  • degree measure
  • radian
  • sine
  • cosine
  • tangent
  • cotangent
  • secant
  • cosecant
  • unit circle
  • standard position
  • terminal side

Questions and answers on Trigonometry — Finding the Measure of an Angle in Terms of One of its Trigonometric Ratios - 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

إذا كان قا θ = 2 وكانت θ زاوية حادة، فإن قياس الزاوية θ يساوي:

  • 1 30°
  • 2 45°
  • 3 60°
  • 4 90°
2

إذا كان قتا θ = 2 وكانت θ زاوية حادة، فإن قياس الزاوية θ يساوي:

  • 1 30°
  • 2 45°
  • 3 60°
  • 4 90°
3

إذا كان ظا θ = −1 وكانت θ في الربع الرابع، فإن قياس الزاوية θ يساوي:

  • 1 45°
  • 2 135°
  • 3 225°
  • 4 315°
4

إذا كان ظا θ = −1 وكانت θ في الربع الثاني، فإن قياس الزاوية θ يساوي:

  • 1 45°
  • 2 135°
  • 3 225°
  • 4 315°
5

إذا كان جتا θ = 0.5 وكانت θ في الربع الرابع، فإن قياس الزاوية θ يساوي:

  • 1 60°
  • 2 120°
  • 3 240°
  • 4 300°
6

إذا كان جا θ = −0.5 وكانت θ في الربع الرابع، فإن قياس الزاوية θ يساوي:

  • 1 150°
  • 2 210°
  • 3 300°
  • 4 330°

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