FIND THE VALUES OF THE OTHER FIVE TRIGONOMETRIC FUNCTIONS OF THETA

About "Find the values of the other five trigonometric functions of theta"

Find the values of the other five trigonometric functions of theta :

Here we are going to see how to find the values of the other five trigonometric functions of theta.

Step 1 :

From the given trigonometric ratio, we have to compare  it with one of the formula given below.

sin θ = Opposite side/hypotenuse side

cos θ = Adjacent side/hypotenuse side

tan θ = Opposite side/Adjacent side

cosec θ = Hypotenuse side/Opposite side

sec θ = Hypotenuse side/Adjacent side

cot θ = Adjacent side/Opposite side 

Step 2 :

Now we have to find the missing side from the given known sides.

Step 3 :

By using the above formula, we have find the other trigonometric ratios.

The following examples given below will illustrate the concept.

Example 1 :

If sin A  =  9/15, find the other trigonometric ratios

Solution :

sin θ  =  Opposite side/hypotenuse side

sin A  =  9/15

Opposite side  =  9, Hypotenuse side  =  15

(Hypotenuse side)²  =  (Opposite side)² + (Adjacent side)²

Adjacent side  =  √15² - 9²

  =  √225 - 81

  =  √144

Adjacent side  =  12

cos A  =  Adjacent side/hypotenuse side  =  12/15

tan A  =  Opposite side/Adjacent side  =  9/12

cosec A  =  Hypotenuse side/Opposite side  =  15/9

sec A  =  Hypotenuse side/Adjacent side  =  15/12

cot A  =  Adjacent side/Opposite side  =  12/9

Example 2 :

If cos A  =  15/17, find the other trigonometric ratios

Solution :

cos θ  =  Adjacent side/hypotenuse side

cos A  =  15/17

Adjacent side  =  15, Hypotenuse side  =  17

(Hypotenuse side)²  =  (Opposite side)² + (Adjacent side)²

Opposite side  =  √17² - 15²

  =  √289 - 225

  =  √64

Opposite side  =  8

sin A  =  Opposite side/hypotenuse side  =  8/17

tan A  =  Opposite side/Adjacent side  =  8/15

cosec A  =  Hypotenuse side/Opposite side  =  17/8

sec A  =  Hypotenuse side/Adjacent side  =  17/15

cot A  =  Adjacent side/Opposite side  =  15/8

Example 3 :

If sec θ  =  17/8, find the other trigonometric ratios

Solution :

sec θ  =  Hypotenuse side/Adjacent side

sec θ  =  17/8

Hypotenuse side  =  17, Adjacent side  =  8

(Hypotenuse side)²  =  (Opposite side)² + (Adjacent side)²

Opposite side  =  √17² - 8²

  =  √289 - 64

  =  √225

Opposite side  =  15

sin θ  =  Opposite side/hypotenuse side  =  15/17

cos θ  =  Adjacent side/hypotenuse side  =  8/17

tan θ  =  Opposite side/Adjacent side  =  15/8

cosec θ  =  Hypotenuse side/Opposite side  =  17/15

cot θ  =  Adjacent side/Opposite side  =  8/15

After having gone through the stuff given above, we hope that the students would have understood "Find the values of the other five trigonometric functions of theta". 

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