IIT JEE , AIEEE Forum - Mathematics , Trignometry

adityagv1729

is sin 90 exactly equal to 1

amitp91

rudra.panda

REJAULMA

hello dear.

1. actually in a right angle triangle ,sin θ = P/ H ,

when θ tends to 90 deg , that time , length of perpendicular is equal to the length of hypotenuse, so P = H

Thus sin θ = 1 , when θ = 90.deg

From the desk of : R. Mkashud Sir.

hsbhatt

The confusion arises because you are still holding on to the definition of the trigonometric ratios in terms of the right triangle. From being mere ratios relating to acute angles, sine, cosine, tangent are extended to being functions of real numbers by mapping the angles to radians i.e the distance traversed on the unit circle.

The definition also changes. Take the right-handed orthogonal cartesian coordinate system. Consider a ray OP making an angle $\theta$ radians with the +ve x-axis (positive angle measured anti-clockwise). Take any point (x,y) on ray OP.

Then $\cos \theta = \frac{x}{r}$ and $\sin \theta = \frac{y}{r}$

The angle 90⁰ corresponds to the number $\frac{\pi}{2}$ . Furthermore the ray making an angle $\frac{\pi}{2}$ with the positive x-axis corresponds to the +ve y-axis in the coordinate system. Any point on the y-axis has the coordinates (0,y). Here r = |y| = y

Hence $\cos \theta = \frac{x}{r}$ = 0 and $\sin \theta = \frac{y}{r}$ = 1

Protyush_Sahu

There is no guarantee that sin 90 = 1

But as there is guarantee that cos 90 = 0

and sin^2a + cos^2a = 1

Hence we get that Sin 90 = 1

hsbhatt

back to square one

(Sigh!)

PS: Do you guys actually read the posts of others before you or you just see the query and jump headlong into answering it?

Protyush_Sahu

It is not like that i knew about it earlier

one suggestion- plz. donot think that ur d 1 who knows every thing

hsbhatt

ok, whatever

Protyush_Sahu

I know whatever I told might have hurt you but even ur comment has hurt me

Mathematics is something which i donot study for marks or for iit. I study maths because i love it a lot.And as far as my sol. is concerned it is solely a product of my brain

Sorryyyyyy ! IF I HAD HURT U IN ANYWAY

hsbhatt

Well, I only have this to say: If I had taken umbrage at every insulting comment I got from my teachers I wouldnt have got through JEE. Because they were not meant to be personal. The wise student will take it as a sign to pull up one's socks to meet the expectations.

Good luck!

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