Question

if sin theta =11/61 find the values of cos theta using trigonometric identity. Please let me know the whole process

Answer 1

sin¢=11/61=perpendicular/hypotenuse

so base =√(61)^2-(11)^2 =60


so we know that cos ¢=base /hypotenuse

so we get cos¢=60/61

hope it's helpful to you....

Answer 2

Answer: cosθ= $\frac{60}{61}$, when sinθ= $\frac{11}{61}$

Step-by-step explanation:

Concept: The basic trigonometric identities are sinθ, cosθ and tanθ.

Sinθ and cosθ are related as sin²θ + cos²θ=1.

Now, it is given to us that sinθ=11/61.

Step 1: sinθ=$\frac{11}{61}$

         ⇒sin²θ=$(\frac{11}{61} )^{2}$

Step 2: Now putting on the above relation, sin²θ + cos²θ=1, we get,

                         $(\frac{11}{61} )^{2}$ + cos²θ =1

                     ⇒cos²θ = 1 - $(\frac{11}{61} )^{2}$

                     ⇒cos²θ = $\frac{61^{2} - 11^{2} }{61^{2} }$

                   ⇒cos²θ = $\frac{(61+11)(61-11)}{61^{2} }$ (from the formula, (a² - b²)=(a+b)(a-b))

                    ⇒cos²θ = $\frac{72*50}{61^{2} }$

                    ⇒cos²θ = $\frac{3600}{61^{2} }$ = $\frac{60^{2} }{61^{2} }$

                    ⇒ cosθ = $\frac{60}{61}$

Final ans: Using the trigonometric identity sin²θ + cos²θ=1, we get the value of cosθ to be $\frac{60}{61}$, when sinθ= $\frac{11}{61}$