Teaching trigonometry

Erlina R. RondaUP NISMED

Teaching trigonometry through problem solvingAn introductory lesson on tangent and cotangent

Erlina R Ronda http://keepingmathsimple.wordpress.com

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How would you determine the width of a river if you cannot measure it directly? You cannot cross the other side, too, but you have with you a meterstick and a big protractor.

PROBLEM


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Solution 1: using 45-degree angle

river

x = k

x

k45o


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Solution 2: congruent triangles

river

mo

mo

k

b

x

x = b


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Solution 3: using 60 or 30-degree angle

river x

k

60o

3kx


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Solution 4: similar triangle, geometric mean

riverx

ka

x

a

k

x

mo90o - mo

akx 2


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Solution 5: similar triangle

riverx

k ab

b

a

k

x

mo

b

akx


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Solution 6: similar triangle

riverx

k

a

b

b

a

k

x

mo

mo

b

akx


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Questions for discussion

1) Which solution do you like most? Like least? WHY?

2) What quantities are involved in the solutions?

3) Which quantities are related as

function?

4) How can other cases be generated for this function?

5) What are other ways of representing this function?

Through use of grid and protractor, students can get the value of the ratios


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38.06

540

40o

2.15

650

Relationship 1: angle →opp/adj

2.15

640

38.06

550

Relationship 2: angle →adj/opp


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Table of valuesAngles(in degrees)

30 40 45 50 60

Value of the ratio of opp/adj

0.58 0.84 1.0 1.19 1.73

Value of the ratio of adj/opp

1.73 1.19 1.0 0.84 0.58

13Erlina R Ronda http://keepingmathsimple.wordpress.com

14Erlina R Ronda http://keepingmathsimple.wordpress.com


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Going back to the initial problem …

• How will you use the idea of the ratio of the shorter sides in a right triangle to solve the problem about the width of the river?

• How does this solution compare with the one using similar triangles?


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Let g: x →

This mapping is called the

cotangent function. It is

defined by the equation

cotangent x = g(x)

or cotangent x = .

Given rtΔABC. Let A = xo

side opposite A = a;side adjacent to A = b.

Let f: x →

This mapping is called the tangent function. It isdefined by the equation

tangent x = f(x)

or tangent x = .

A

B

C

a

b

xo

b

a

b

a

a

b

a

b

Teaching trigonometry

Education

Transcript of Teaching trigonometry