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Home >> Trigonometry Ratios >> Examples

Find ratio of Sin, Cosec, Cos, Sec, Tan and Cot - Trigonometry : Solved Examples

T Ratios of Angles - 30, 45, 60 & 90 degree angles Find Height, Distance using T - Ratios

If cos Theta = 2/3, find sin and tan theta
Lets draw the right angle triangle with the above mentioned details

Given thing are
cos Θ = 2/3

we know that Cos Θ = Adjacent Side / Hypotenuse, so we get

Adjacent Side = 2
Hypotenuse = 3



Hypotenuse : BC = 3
Adjacent Side : AB = 2 (Adjacent to ∠ Θ)
Opposite Side : AC = ? (Opposite to ∠ Θ)

To find the Opposite Side - AC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)2 + (Leg 2)2)

 ____________
AC = √ BC2 - AB2 


 ____________
AC = √ 32 - 22 


 ____________
AC = √ 9 - 4 


 __
AC = √ 5 


Now we will try to simplify square root of 5. As no pairs can be made the final value will be

 __
AC = √  5  


So Sin, Cos and Tan will be as follows -

Sin Θ = Opposite Side / Hypotenuse
 __
Sin Θ = √ 5  / 3


Tan Θ = Opposite Side / Adjacent Side
 __
Tan Θ = √ 5  / 2


Cos Θ = Adjacent Side / Hypotenuse
Cos Θ = 2/3

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