trig question?

Question

In a problem I'm doing it says that 1-sin^2(x) = cos^2(x)

can anyne tell me why this is/where it comes from?
thanks

Answer 1

This is one form of a very basic identity (sin^2 θ + cos^2 θ = 1); it's pretty clear from the definition of sin and cos either from a right-angle triangle or from the unit circle.

Take a right-angle triangle with angle θ and side lengths o opposite it, a adjacent to it and h hypotenuse:
sin θ = o/h, cos θ = a/h
sin^2 θ + cos^2 θ = o^2 / h^2 + a^2 / h^2
= (o^2 + a^2) / h^2
= h^2 / h^2 from Pythagoras
= 1.

From the unit circle, we define the point on the unit circle generated by an angle θ anticlockwise from the positive x-axis to be (cos θ, sin θ). But since it is on the unit circle, with equation x^2 + y^2 = 1, it must satisfy cos^2 θ + sin^2 θ = 1.

Answer 2

This is a trigonometric identity. I'm hoping you've studied the unit circle at some point, or this may not make sense. I'll run through it briefly and see how we go.

Basically, you draw a circle with a radius of 1 unit. If you then measure an angle around from the positive x-axis, you can place another line anywhere in the circle with angle 'x'. The co-ordinates of the point where this line intersects the boundary of the circle are (cos(x),sin(x)).

If you then form a triangle between this point and the x-axis, you can see that the horizontal displacement is equal to cos(x), and the vertical displacement is sin(x). You then use pythagoras' theorem, as the radius of the circle is 1, sin^2(x) + cos^2(x) = 1, or in other terms, 1 - sin^2(x) = cos^2(x).

Hope this makes sense!

Answer 3

Well,if you add the sin square of any angle with that of cos square of the same angle ,the total is always 1.
Hence in trigonmentry,we use the identity sin^2 +cos^=1
Basing on this ,we also use the following identities
sin^2=1-cos^2
sin=sqrt(1-cos^2)
cos^2=1-sin^2
cos=sqrt(1-sin^2)

Answer 4

The basic equation of trigonometry is: sin^2(x)+cos^2(x)=1. This is from where trigonometry starts. I'm pretty sure you can find the proof of this equation in all trigonometry books.
If you organize a little this basic equation, you'll get exactly 1-sin^2(x)=cos^2(x).

Answer 5

one way of doing it is to say cos(x) = opposite over hypotenuse ( you can make your own right angled triangle)
sin x = adjacent side over hypotenuse and use pythagoras
hypotenuse^2 = sum of squares of the other sides

so h^2 = o^2 +a^2 , 1 = o^2/h^2 + a^2/h^2 = cos^2 + sin^2

Answer 6

check at this website