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
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