Activity1 Basic Trignometric Ratios

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Objectives

Students will be able to identify the adjacent/opposite side, with respect to theta and the hypotenuse of a triangle and define the six trigonometric ratios of an acute angle of triangle.

Estimated Time

40 minutes

Prerequisites/Instructions, prior preparations, if any

Meaning of ratio,know about hypotenuse, short leg, long leg,right angle and vertices of right triangle and how to measure side and angle by using ruler and Protractor and also how to convert angle measure from degree to radians and radians to degree.

Materials/ Resources needed

Digital - Click here to open the file

Non digital - Protractor,ruler.

Process (How to do the activity)


Download this geogebra file from this link.


Activity:

  1. let us consider one right angle triangle and write the possible ratios of its sides with respect to its acute angle.
  2. Triangle has 3 sides.Using the sides of triangle,we can have six different ratios.(To write the ratio(fraction)numerator can be written in 3 ways and denominator in 2 ways, both can be written in 3*2=6 ways)
  3. Identify the name of the ratios in Trigonometry.
  4. Measure adjacent side ,opposite side and hypotenuse in a given triangle and record it on the table
Ratio Trigonometric names for the ratios Values of the trigonometric ratio for the angle
AC/CE

= Opposite side / Hypotenuse

Sine of angle θ
AE/CE =

Adjacent side / Hypotenuse

Cosine of angle θ
AC/AE

=Opposite side / Adjacent side

Tangent of angle θ
CE/AC

=Hypotenuse / Opposite side

Cosecant of angle θ
CE/AE

=Hypotenuse / Adjacent side

Secant of angle θ
AE/AC

=Adjacent side / Opposite side

Cotangent of angle θ

Evaluation at the end of the activity

  1. Find the six trigonometric ratios of the triangle?
  2. Find the measure of each trigonometric ratios of the triangle?

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