मराठी
महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता १० वी

If `Cos Theta = 5/13` Where `Theta` Is an Acute Angle. Find the Value of `Sin Theta`

Advertisements
Advertisements

प्रश्न

if `cos theta = 5/13` where `theta` is an acute angle. Find the value of `sin theta`

Advertisements

उत्तर

`cos theta = 5/13`

`sin^2 theta = 1 - cos^2 theta = 1 - 25/169 = 144/169`

`sin theta = +- 12/13` as `theta` is acute, therefore `sintheta` must be positive

`:. sin theta  = 12/13`

 

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
2017-2018 (March) Set A

संबंधित प्रश्‍न

Prove the following trigonometric identities.

`"cosec" theta sqrt(1 - cos^2 theta) = 1`


Prove the following trigonometric identities.

`(1 + cos A)/sin^2 A = 1/(1 - cos A)`


Prove the following identities:

`1/(1 + cosA) + 1/(1 - cosA) = 2cosec^2A`


Prove the following identities:

`sinA/(1 + cosA) = cosec A - cot A`


Prove the following identities:

`((cosecA - cotA)^2 + 1)/(secA(cosecA - cotA)) = 2cotA`


`(sectheta- tan theta)/(sec theta + tan theta) = ( cos ^2 theta)/( (1+ sin theta)^2)`


If `tan theta = 1/sqrt(5), "write the value of" (( cosec^2 theta - sec^2 theta))/(( cosec^2 theta - sec^2 theta))`.


From the figure find the value of sinθ.


If sec2 θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.


If sin θ + sin2 θ = 1, then cos2 θ + cos4 θ = 


Prove the following identity :

`(cosA + sinA)^2 + (cosA - sinA)^2 = 2`


Prove the following identity : 

`sin^4A + cos^4A = 1 - 2sin^2Acos^2A`


Prove that `(tan θ)/(cot(90° - θ)) + (sec (90° - θ) sin (90° - θ))/(cosθ. cosec θ) = 2`.


Prove that `sin A/(sec A + tan A - 1) + cos A/(cosec A + cot A - 1) = 1`.


Prove that `tan^3 θ/( 1 + tan^2 θ) + cot^3 θ/(1 + cot^2 θ) = sec θ. cosec θ - 2 sin θ cos θ.`


Prove that sin2 5° + sin2 10° .......... + sin2 85° + sin2 90° = `9 1/2`.


If sin θ + cos θ = `sqrt(3)`, then prove that tan θ + cot θ = 1.


If a cos θ – b sin θ = c, then prove that (a sin θ + b cos θ) = `±  sqrt(a^2 + b^2 - c^2)`


If tan α + cot α = 2, then tan20α + cot20α = ______.


If 2sin2θ – cos2θ = 2, then find the value of θ.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×