Question

find the principal value of cos^-1 (sin 10π/7)​

Answer 1

Answer:

4pi/7

Step-by-step explanation:

cos^_1(cos(2pi- 10pi/_7)= 4pi/7

Answer 2

Answer:

$\frac{13\pi }{14}$

Step-by-step explanation:

Given:- $cos^{-1}(sin\frac{10\pi }{7} )$

To Find:- Principal value of the above equation.

Solution:-

As we know acc. to trigonometric formulas,

                       sin θ = cos( 90° -  θ)

∴ sin $\frac{10\pi }{7}$ = cos($\frac{\pi }{2} - \frac{10\pi }{7}$)

              = $cos (\frac{7\pi - 20\pi }{14} )$

              = $cos(-\frac{13\pi }{14} )$

As we know, cos (- θ) = cos θ

∴ $cos (-\frac{13\pi }{14} )$ = $cos (\frac{13\pi }{14} )$

Now, the equation becomes,

$cos^{-1} (cos(\frac{13\pi }{14} ))$ = $\frac{13\pi }{14}$

Hence, the answer is $\frac{13\pi }{14}$

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