Question

If cosx is approximately 0.9511, what is the measurement of x to the nearest degree? Approximately, what is the sin of the angle that is complementary to x?

Answer 1

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 2

Answer: Value of x = 18° and

complementary to x i.e. sin 72°

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°