Verified Answer :

I used the calculator assigning various values of x to get 0.9511.

cos x = 0.9511 
cos 18° = 0.9511
sin and cos are complementary angles = 90° - 18° = 72°

sin 72° = 0.9511

sin 72° = cos 18

Answer: Value of x = 18° and

complementary to x i.e. sin 72°

Step-by-step explanation:

Since we have given that

\(\cos x=0.9511\)

We need to the find the measurement of x to the nearest degree.

For this we will use " Inverse trigonometric ratios ":

\(x=\cos^{-1}(0.9511)\\\\x=17.99\textdegree \\\\x=18\textdegree\ approx.\)

Since Sine of the angle that is complementary to x .

So,

\(\sin (90\textdegree-18\textdegree)=\sin 72\textdegree\\\)

Hence, value of x = 18° and

Complementary to x i.e. sin 72°

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