TRIGONOMETRIC RATIOS SIN COS AND TAN
About "Trigonometric ratios sin cos and tan"
Trigonometric ratios sin cos and tan :
In the right triangle, we refer to the lengths of the three sides according to how they are placed in relation to the angle θ
- The side that is opposite to the right angle is called the Hypotenuse. This is the longest side in a right triangle.
- The side that is opposite to the angle θ is called the Opposite side.
- The side that runs alongside the angle θ and which is not the Hypotenuse is called the Adjacent side.
We can form six ratios with the sides of a right triangle.
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
tan θ = Adjacent side / Opposite side
Trigonometric ratios sin cos and tan - Examples
Example 1 :
Find the cosine ∠C
Solution :
Formula to find cos θ is Adjacent side / Hypotenuse side
Here θ has to be considered in the place of ∠C
90° is at ∠A. So the side which is opposite to 90° is known as hypotenuse side. The side which is opposite to θ (∠C) is known as opposite side. The remaining side is known as adjacent side.
BC = hypotenuse side = 17
AB = opposite side = 8
AC = Adjacent side = 15
cos C = 15/17
Example 2 :
Find the sin ∠A
Solution :
Formula to find sin θ is Opposite side / Hypotenuse side
Here θ has to be considered in the place of ∠A.
AC = hypotenuse side = 65
BC = opposite side = 33
AB = Adjacent side = 56
sin C = 33/65
Example 3 :
Find the tan ∠B
Solution :
Formula to find tan θ is Opposite side / Adjacent side
Here θ has to be considered in the place of ∠B.
BC = hypotenuse side = 5
AC = opposite side = 4
AB = Adjacent side = 3
tan A = 4/3
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