Activity1 Basic Trignometric Ratios
Contents
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:
- let us consider one right angle triangle and write the possible ratios of its sides with respect to its acute angle.
- 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)
- Identify the name of the ratios in Trigonometry.
- 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
- Find the six trigonometric ratios of the triangle?
- Find the measure of each trigonometric ratios of the triangle?
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