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Trigonometry Ratios

What are the ones we know so far and are there

any more?

When you were first introduced to Trigonometry

Tan ? ?

It was

Cos ? ?

adjacent

adjacent

Sin? ?

OR

OR

Hypotenuse

opposite

Hypotenuse

And then you used them to find the unknown side

or angle

opposite

But why limit ourselves to comparing the sides in

these ways?

You remembered all of this by

S

O

H

C

A

H

T

O

A

OR

Silly Old Hags Cant Always Hide Their Old Age.

What would happen if we compared the sides

differently to SOHCAHTOA?

Instead of comparing

Why not compare

OPPOSITE

to

ADJACENT

ADJACENT

to

OPPOSITE

ADJACENT

OPPOSITE

which is Tan ??

But if we compare the sides this way

The Tan ratio is

This new way of comparing these sides is the.

RECIPROCAL

of the Tan Ratio

is remembered as

the Cotangent Ratio

The same thing can be done for Sine Cosine

is the Reciprocal of the Cosine Ratio

is remembered as

the Secant Ratio

is the Reciprocal of the Sine Ratio

is remembered as

the Cosecant Ratio

How can these new ratios be used?

You can be given a triangle and asked to simply

give the value of the Cotangent, Secant or

Cosecant of an angle, expressed as a fraction

You can also be asked to give the EXACT VALUE of

the Cotangent, Secant or Cosecant of an angle.

e.g.

Find the value of Secant 30?

e.g.

Sec 30?

What is the value of Cosec B?

Cosec B

Remember you can only be asked for an exact value

if the angle is related to 30?, 45? or 60?

You could be asked to find the Cotangent, Secant

or Cosecant of an angle for which you would

normally use your calculator

And lastly

Find the value of Secant 37?

e.g.

Unfortunately, there are no calculator keys for

these ratios!

?

So you have to find the decimal value from

calculator and then either use the reciprocal key

or store it in the calculators memory and then

divide it into 1

1

Sec 37?

Cos 37?

?

?

1.252

to 3 d.p.