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If sintheta = (3)/(5), then find the val...

If `sintheta = (3)/(5)`, then find the value of `tantheta and sectheta`.

Text Solution

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Given, `sintheta = (3)/(5)`
Let AOB be the right traingle such that, `angleOAB=theta`. ,
Assume that OB = 3 and AB = 5 (see fig. 8.5).
Then, `OA= sqrt( AB^(2)-OB^(2))=sqrt(25-9)= 4`.
So, `tantheta = ("Side opposite to " theta)/("Side adjacement to " theta)=(OB)/(OA)=(3)/(4)` and ,
`sectheta = ("Hypotenuse")/("Side adjacement to " theta)=(AB)/(OA)=(5)/(4)`.
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Knowledge Check

  • Find the value of sintheta in terms of sectheta .

    A
    `(1)/(sqrt(sec^(2)-1))`
    B
    `(sec^(2)theta)/(sqrt(sec^(2)-1))`
    C
    `sqrt(sec^(2)theta-1)/(sectheta)`
    D
    `sqrt(sec^(2)theta-1)`

  • If sectheta+tantheta=2 , then find the value of sintheta .

    A
    `(3)/(5)`
    B
    `(2)/(3)`
    C
    `-(3)/(5)`
    D
    `-(2)/(5)`

  • If sintheta=(3)/(5) , then the value of (tantheta+costheta)/(cottheta+cosectheta) is equal to

    A
    `(29)/(60)`
    B
    `(31)/(60)`
    C
    `(34)/(60)`
    D
    `(37)/(60)`

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