Root 3 over 2.
To simplify the expression sin(30°) cos(90°) sin(90°) cos(30°), we first evaluate the trigonometric functions at the given angles. sin(30°) = 1/2, cos(90°) = 0, sin(90°) = 1, and cos(30°) = √3/2. Substituting these values into the expression, we get (1/2) * 0 * 1 * (√3/2) = 0. Therefore, the final result of sin(30°) cos(90°) sin(90°) cos(30°) is 0.
The cosine of 15 degrees can be calculated using the cosine subtraction formula: ( \cos(15^\circ) = \cos(45^\circ - 30^\circ) ). This gives us ( \cos(15^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ ). Plugging in the known values, ( \cos 45^\circ = \frac{\sqrt{2}}{2} ), ( \cos 30^\circ = \frac{\sqrt{3}}{2} ), ( \sin 45^\circ = \frac{\sqrt{2}}{2} ), and ( \sin 30^\circ = \frac{1}{2} ), we find that ( \cos 15^\circ = \frac{\sqrt{6} + \sqrt{2}}{4} ).
cos(30 deg) = sqrt(3)/2 = 0.8660 approx.
Cosine(90) = 0 NB Cosine(0) = 1 Cos(30) = 0.8669... Cos(45) = 0.7071... Cos(60) = 0.5 Cos(90) = 0 Cos(120) = -0.5 Cos(0135) = -0.7071... Cos(150) = -0.8660... Cos(180) = -1 NB #1 ; refer to your (scientific) calculator or #2 ; refer to Castles Four Figures Tables. NNB Note the negatives (-) between 90 & 180.
As a first step, I would convert everything to sines and cosines. sin x cot x = sec x - cos x thus becomes: (sin x) (cos x / sin x) = (1 / cos x) - cos x Simplifying: cos x = 1 / cos x - cos x It doesn't look as though they are equal. In fact, if you do the calculations for some specific angle, e.g. 30 degrees, you see that they are not.
cos(30 = 0.8660254038
cos(30)cos(55)+sin(30)sin(55)=cos(30-55) = cos(-25)=cos(25) Note: cos(a)=cos(-a) for any angle 'a'. cos(a)cos(b)+sin(a)sin(b)=cos(a-b) for any 'a' and 'b'.
Cos(30) = sqrt(3)/2
Cos(30) = sqrt(3)/2 = 0.866025403..
0.866
cos(30) is an irrational number and so cannot be expressed as a rational fraction. It is (√3)/2.
To simplify the expression sin(30°) cos(90°) sin(90°) cos(30°), we first evaluate the trigonometric functions at the given angles. sin(30°) = 1/2, cos(90°) = 0, sin(90°) = 1, and cos(30°) = √3/2. Substituting these values into the expression, we get (1/2) * 0 * 1 * (√3/2) = 0. Therefore, the final result of sin(30°) cos(90°) sin(90°) cos(30°) is 0.
sin(30) = sin(90 - 60) = sin(90)*cos(60) - cos(90)*sin(60) = 1*cos(60) - 0*sin(60) = cos(60).
The cosine of 15 degrees can be calculated using the cosine subtraction formula: ( \cos(15^\circ) = \cos(45^\circ - 30^\circ) ). This gives us ( \cos(15^\circ) = \cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ ). Plugging in the known values, ( \cos 45^\circ = \frac{\sqrt{2}}{2} ), ( \cos 30^\circ = \frac{\sqrt{3}}{2} ), ( \sin 45^\circ = \frac{\sqrt{2}}{2} ), and ( \sin 30^\circ = \frac{1}{2} ), we find that ( \cos 15^\circ = \frac{\sqrt{6} + \sqrt{2}}{4} ).
The cosine of 15 degrees can be calculated using the cosine subtraction formula: (\cos(15^\circ) = \cos(45^\circ - 30^\circ)). This gives us (\cos(15^\circ) = \cos(45^\circ)\cos(30^\circ) + \sin(45^\circ)\sin(30^\circ). Substituting the known values, (\cos(45^\circ) = \frac{\sqrt{2}}{2}), (\cos(30^\circ) = \frac{\sqrt{3}}{2}), (\sin(45^\circ) = \frac{\sqrt{2}}{2}), and (\sin(30^\circ) = \frac{1}{2}), we find that (\cos(15^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4}).
cos 60
cos(60) = 0.57 x 60 x cos(60) = 7 x 30 = 210