Is cos1 transcendental?

If cos1 is algebraic, so is sin1=√1−cos21. Thus ei=cos1+isin1 is algebraic. But, by Lindemann’s theorem, eα is transcendental whenever α is a nonzero algebraic number.

Is sin 1 degree algebraic?

You will get a polynomial in cos(1), in which every power of cos(1) is even. So, substitute cos2(1)=1−sin2(1), and you get a polynomial in sin(1) which equals to 0. Hence sin(1) is algebraic over Q.

Which is bigger sin1 or cos1?

In general, for x<=π/2, as x increases, cos x decreases, sin x increases and tan x increases. Now, for x<=π/4, cos x>sin x. At x=π/4, sin x= cos x. For x>π/4, sin x>cos x, so sin 1>cos1.

Is Cos transcendental?

Examples include the functions log x, sin x, cos x, ex and any functions containing them. Such functions are expressible in algebraic terms only as infinite series.

What is the difference between sin 1 degree and sin 1?

i.e. sin 1 is greater than sin 1 degree.

Which is greater sin1 or tan1?

So, sin-11 is the greatest value.

Which is greater sin or cos?

We can see that the value of sin increases from 0 to 90 degrees and it is vice versa for cos I.e., it decreases form 0 to 90. The value of sin and cos are same at 45 degree. definitely cos 40 is greater than sin 40.

Is Sinx transcendental?

How do you simplify sin(cos−1 x)?

How do you simplify sin(cos−1 x)? Let’s draw a right triangle with an angle of a = cos−1(x). As we know cos(a) = x = x 1 we can label the adjacent leg as x and the hypotenuse as 1. The Pythagorean theorem then allows us to solve for the second leg as √1 −x2.

What is the difference between cos 1 and cos 1 degrees?

The difference lies in the fact that in cos 1 angle is in radian and in cos 1 degree, angle is one degree. 360 degrees is 2pi radian, so one degree= 2pi/360 radians i.e 0.01745 radians. So it is where the difference arises. , B.Tech Mechanical Engineering & Design, Indian Institute of Information Technology, Design and Manufacturing,…

What is the range of cos^-1 x?

The range of cos^-1 (x) is [0,π]. Cheers!!! What is the difference between cos 1 and cos1°? The difference lies in the fact that in cos 1 angle is in radian and in cos 1 degree, angle is one degree. 360 degrees is 2pi radian, so one degree= 2pi/360 radians i.e 0.01745 radians.

How do you find sin(cos^ (-1)(x)) using the Pythagorean theorem?

The Pythagorean theorem then allows us to solve for the second leg as sqrt (1-x^2). With this, we can now find sin (cos^ (-1) (x)) as the quotient of the opposite leg and the hypotenuse. sin (cos^ (-1) (x)) = sin (a) = sqrt (1-x^2)/1 = sqrt (1-x^2)