MYTUTOR SUBJECT ANSWERS

390 views

Why is it that sin^2(x) + cos^2(x) = 1?

Let's start with the definition of sin(x) and cos(x). We're going to use rather than x here to avoid confusion, but the idea is exactly the same.

Take a unit circle - that is, a circle with centre (0,0) and radius 1 - and pick any point on it. Let the co-ordinates of this point be (x,y). Now draw a line from the origin to your point. Start from the point, and move the (real or imaginary) pencil round clockwise until you reach (1,0) on the positive x-axis. What you've just drawn is t, which is the angle between your line and the positive x-axis.

By definition, x = cos(t) and y = sin(t). So the co-ordinates of your point could equally be written (cos(t), sin(t)).

Now we can form a right-angled triangle with side lengths x, y and 1. It's clear from this that x2 + y21, or in other words, cos2(t) + sin2(t) = 1 for all values of t. Here is a diagram to clarify: goo.gl/YuLWqe

You sometimes see this written as cos2(t) + sin2(t) ≡ 1. The "triple bar" equals sign just emphasises that it is true for all values of t.

John T. GCSE Maths tutor, A Level Maths tutor

1 year ago

Answered by John, who tutored A Level Maths with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

183 SUBJECT SPECIALISTS

£20 /hr

Jack G.

Degree: Politics, Philosophy, and Economics (Bachelors) - Warwick University

Subjects offered: Maths, Religious Studies+ 2 more

Maths
Religious Studies
Economics
.TSA. Oxford.

“Hello, I'm Jack and am studying politics, philosophy, and economics at Warwick.  Having recently been through the subjects I'm looking to tutor I feel like I know first hand what difficulties you'll be facing. I always found I wanted ...”

MyTutor guarantee

£20 /hr

Shaun F.

Degree: Mathematics with International Study (Masters) - Exeter University

Subjects offered: Maths

Maths

“Hi, I'm Shaun! I'm currently studying for a masters in Mathematics at the University of Exeter..”

MyTutor guarantee

£20 /hr

Alexandra L.

Degree: Aeronautical and Aerospace Engineering (Bachelors) - Leeds University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“About Me I’m an Aerospace Engineering student at Leeds University. I have long loved tinkering and seeing how things work; to me, science is just the formal extension of this curiosity. Throughout sixth form I helped run the school ...”

About the author

£20 /hr

John T.

Degree: Japanese (Bachelors) - Oxford, Pembroke College University

Subjects offered: Maths

Maths

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Other A Level Maths questions

The variable x=t^2 and the variable y=2t. What is dy/dx in terms of t?

Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

How/when should I use the product rule for differentiation?

Simplify (7+sqrt(5))/(sqrt(5)-1), leaving the answer in the form a+b*sqrt(5)

View A Level Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok