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The sine is almost equal to the angle, in case the angle is expressed in radians. Please make a picture of a circle, put a point on the circle at a small angle (say, 10 degrees or less), then draw the sine (a vertical line from the x-axis up to your point) for a small angle. You will see that the arc of the circle has almost the same length as the vertical line you drew. The arc is the angle; the vertical line is the sine.

Q: Why sin angle equal to angle if the angle is very small?

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The sine of an angle of a right triangle - which is a triangle containing one 90o angle - is calculated as the length of the side opposite the angle divided by the length of the hypotenuse. For very small values of x, sin(x) is approximately equal to x.

Let ABC and DEF be triangles which are right angled at A and D, such that the hypotenuses BC and EF are equal and, without loss of generality, angle B = angle E.ThenThen by the sine rule, BC/sin(A) = AC/sin(B) and EF/sin(D) = DF/sin(E)Since angle A = angle D = pi/2 radians, then sin(A) = sin(D) = 1so that BC/sin(A) = BC while EF/sin(D) = EFtherefore, since the hypotenuses BC and EF are equal, the left hand sides of the two equations are equal.Therefore, AC/sin(B) = DF/sin(E)then, since angle B = angle E, then sin(B) = sin(E) so that AC = DF.Also, angle C = pi/2 - angle Band angle F = pi/2 - angle Ethe right hand sides are equal so angle C = angle F.Then in a manner similar to the above, we can show that AB = DE.Thus all three pairs of corresponding sides are equal and all three pairs of corresponding angles are equal so that the two triangles are congruent.

the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c

Yes. The derivation of the simple formula for the period of the pendulum requires the angle, theta (in radians) to be small so that sin(theta) and theta are approximately equal. There are more exact formulae, though.

Not exactly, the angle of refraction = the angle of incidence, which means the ratio of sine of angle of incidence to the sine of angle of refraction is constant for two media. That is sin i /sin r = constant , and this constant is called refractive index

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No. Sin of any angle is always less than or equal to 1.

The sine of an angle of a right triangle - which is a triangle containing one 90o angle - is calculated as the length of the side opposite the angle divided by the length of the hypotenuse. For very small values of x, sin(x) is approximately equal to x.

45 degree

Let ABC and DEF be triangles which are right angled at A and D, such that the hypotenuses BC and EF are equal and, without loss of generality, angle B = angle E.ThenThen by the sine rule, BC/sin(A) = AC/sin(B) and EF/sin(D) = DF/sin(E)Since angle A = angle D = pi/2 radians, then sin(A) = sin(D) = 1so that BC/sin(A) = BC while EF/sin(D) = EFtherefore, since the hypotenuses BC and EF are equal, the left hand sides of the two equations are equal.Therefore, AC/sin(B) = DF/sin(E)then, since angle B = angle E, then sin(B) = sin(E) so that AC = DF.Also, angle C = pi/2 - angle Band angle F = pi/2 - angle Ethe right hand sides are equal so angle C = angle F.Then in a manner similar to the above, we can show that AB = DE.Thus all three pairs of corresponding sides are equal and all three pairs of corresponding angles are equal so that the two triangles are congruent.

nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees nwater * sin 30=nair *sin(angle of refraction) 1.33*0.5=1*sin(angle of refraction) sin(angle of refractiob)=0.665 angle of refraction inair=41.6 degrees

the sine rule, angle (a) and opposite length is eaqual to angle (b) and opposite length. which are also equal to angle (c) and opposite length. Sin A = Sin B = Sin C ------- -------- ---------- a -------- b -------- c

Assuming the angle is given in radians, it is -0.9939

Yes. The derivation of the simple formula for the period of the pendulum requires the angle, theta (in radians) to be small so that sin(theta) and theta are approximately equal. There are more exact formulae, though.

sin312 the terminal angle of 312 is equal to 48 degrees! That's all i know!

Not exactly, the angle of refraction = the angle of incidence, which means the ratio of sine of angle of incidence to the sine of angle of refraction is constant for two media. That is sin i /sin r = constant , and this constant is called refractive index

we should keep the amplitude of simple pendulum small because we have to make a very small angle so that we can neglecting value of sin

Yes. Light follows the law of signs and Sin(I)/vi = Sin(R)/vr . Because vi=vr the angles are equal. This important law in physics is often stated as follows: Angle of Reflection = Angle of Incidence