When, realistically, do people actually use radians and/or trigonometric identities?

Question

A student asked me this today - when, in the real world, are either of these things ever used?

Answer 1

Realistically, they're not used until one teaches or learns the calculus. Although we're so used to dealing with degrees, the actual slopes of tangent lines of graphs of trig functions only work with radians. When you sketch a sine wave in class using 0°, 90°, 180°, and so on as values on your x-axis, it's easy to teach and easy to learn... but if you're trying to show the actual shape of the wave (using equally-sized units for x's and y's), radians are the only way to show their true values.

As far as trig identities go, perhaps in simplifying or substituting in an integral, but that's about all I can think of. :-( They're a great way to show student mastery of rational algebraic expressions, though, and their ability to form informal proofs... good practice for college.

Answer 2

If a person is in any science or engineering related field, then they will use these tools all the time. They are used in designing circuits, designing nuclear reactors, animal population models, heat transfer, economics, building bridges, etc.

Sin and Cos are so fundamental in math they appear in everywhere, and any time they appear they are always in radians.

Answer 3

Anyone who works in the world of digital signal processing (and that's every digital cellphone on the Planet and pretty much all other digital communication systems) thinks in terms of 'phase accumulation' (which is measured in radians)

Anyone who works with servo systems (analog or digital) is always thinking in terms of 'phase lead' and 'phase lag' so that a thing called 'loop instability' won't rear its ugly head.

Anyone who works in surveying uses trig constantly.

And, as Louise said, it's used constantly in 'advanced math'.


Doug

Answer 4

In physics, a common unit of measurement for angular velocity is radians per second.

Answer 5

Surveying.

You can use trig to measure heights/distances you couldnt normally. Get some way to measure an angle and bam, have your students measuring the height of the school or what not.

Answer 6

We used to use them all the time when testing military weapons.

Answer 7

if you are a architect i would imagine alot because you might know the angles but not the sides

Answer 8

as rarely as possible

Answer 9

a million) a million+tan^2x=a million+sin^2x/cos^2x (cos^2x+sin^2x)/cos^2x (same deno.) all of us comprehend that: sin^2x+cos^2x=a million then, a million+tan^2x=a million/cos^2x 2) a million/cos^2x= (sin^2x+cos^2x)/cos^2x a million+cos^2x =sin^2x/cos^2x+cos^2x/cos^2x with: sin^2x/cos^2x=tan^2x then, a million/cos^2x=a million+tan^2x