When you subtract theta from 180 ( if theta is between 90 degrees and 180 degrees) you will get the reference angle of theta; the results of sine theta and sine of its reference angle will be the same and only the sign will be different depends on which quadrant the angle is located. Ex. 150 degrees' reference angle will be 30 degrees (180-150) sin150=1/2 (2nd quadrant); sin30=1/2 (1st quadrant) 1st quadrant: all trig functions are positive 2nd: sine and csc are positive 3rd: tangent and cot are positive 4th: cosine and secant are positive
The sine and cosine of acute angles are equal only for 45° sin45° = cos 45° = 1/sqrt(2) = 0.7071
acute angle is an angle that is less that 90 degrees. An isosceles triangle is a triangle that has 2 equal sides and 2 equal angles.
1/2 the base times the height. If given only the length of equal sides and the angle formed between them, assuming side length 'l' and angle as 'x' square of 'l' multiplied by sine of x divided by 2 It is given by under root 3 divided by 4 multiplied by a2 where "a" is the length of the equal side
They are used to find the angle or side measurement of a right triangle. For example, if 2 sides of a right triangle have known values and an angle has a known measurement, you can find the third side by using sine, cosine or tangent.
sqrt 2 / 2 is the answer.
The arcsine is the angle whose sine is equal to the given value. arcsine is also called sine inverse (sin-1 ) if sin 30o = 1/2 , then sin-1 1/2 = 30o
The angle of depression is equal to the angle of elevation, so use the sine ratio to find the angle. sine = opposite (the vertical drop) divided by the hypotenuse (the ski slope) sine = 100/250 = 2/5 or 0.4 sine-1(0.4) = 23.57817848 degrees which is about 24 degrees
The number 1.414... (square root of 2) is two times the cosine or sine of a 45 degree angle. The reason for this is that for a 45 degree angle, the two sides are cosine and sine, they are equal, and if you solve using the Pythagorean theorem with a hypotenuse of 1, the two sides are each (21/2)/2.
sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)
When you subtract theta from 180 ( if theta is between 90 degrees and 180 degrees) you will get the reference angle of theta; the results of sine theta and sine of its reference angle will be the same and only the sign will be different depends on which quadrant the angle is located. Ex. 150 degrees' reference angle will be 30 degrees (180-150) sin150=1/2 (2nd quadrant); sin30=1/2 (1st quadrant) 1st quadrant: all trig functions are positive 2nd: sine and csc are positive 3rd: tangent and cot are positive 4th: cosine and secant are positive
sin(30) = 1/2
sin 300 = 1/2
Snell's law is related to the phenomenon of refraction. The ratio of the sine of the angle of incidencein theFIRST medium to the sine of the angle of refractionin theSECOND medium would always be a constant and this constant is known to be the refractive index of the second medium with respect to the first one. Refractive index of 2 with respect to 1 = Sine of angle in1 / sine of angle in 2 This is later equated to by Huygens as Refractive index of 2 with respect to 1 = velocity of light in medium1 / velocity of light in medium 2
Divide -900 by 360, and the remainder will be the angle you need to find the sine of: -900 / 360 = -2.5 --> -900 = 360*(-2 - 0.5), so sine(-180°) = sine(-900°). sine(-180°) = 0
Consider a right triangle ABC as shown below. The right angle is at B, meaning angle ABC is 90 degrees. With the editor I have, I am not able to draw the line AC but imagine it to be there. By pythagorean theorem AC*2 = AB*2 + BC*2. The line AC is called the hypotenuse. Consider the angle ACB. The cosine of this angle is BC/AC, the sine is AB/AC and tangent is AB/BC. If you consider the angle BAC, then cosine of this angle is AB/AC, the sine is BC/AC and tangent is BC/AB. In general sine of an angle = (opposite side)/(hypotenuse) cosine of an angle = (adjacent side)/(hypotenuse) tangent of an angle = (opposite side)/(adjacent side) |A | | | | | | |______________________C B
pi/2*(2n-1) radians.