Which Trig Id's do you remember?

Question

Dear all,

I know you can form all the Trig ID's using the addition and half angle formulae. However, which do you find the most useful to remember to save time in exams, when calculating etc.?

Many thanks

Answer 1

These are pretty much all the trig identities you need to know:

sin and cos of 0, 30, 45, 60, 90, 180, 270, 360
(Of course, those angles may be given in terms of radians)
sin(x) is odd and cos(x) is even and how that allows you to calc their values in the other quadrants.
Definitions of tan(x), cot(x), sec(x), csc(x) in terms of sin(x) and cos(x)
Know what the sign (plus or minus) of sin and cos are in each quadrant, and how that determines the sign of every other trig function.

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
Understand how the above let you instantly write down cos(a-b) and sin(a-b) (since sin(-b) = -sin(b) and cos(-b)=cos(b))
The product formulas might be memorized right while you are studying them, but they almost never happen in practise.
cos(2x) = cos²(x) - sin²(x) = 2cos²(x) - 1
sin(2x) = 2sin(x)cos(x)

That's pretty much it. You should know the stuff above cold, and most anything else can be worked out on the spot. I would also be conscious that at 45 + 90k the tan and cot are always plus or minus 1.

Answer 2

All are equally confusing. May be you could remember values of some angles like sin30/cos30, sin45/cos45, sin60/cos60, sin90/cos90. We know formulas very well. What's confusing is +- signs and cos/sin terms. You can check if you are doing it correctly, if you have above values by heart. For eg: if you want sin(A+B)=?(Then check how much is sin(30+60) which you know is equal to sin90) Or if you want sinA+sinB then you know what is sin30+sin60. That's how you will know which terms to be placed where.

Answer 3

The sum formulas are all I usually need.

If I forget anything about 30°, 45° or 60° I just draw a triangle and figure it out.

If I forget about cos2x (and I always do) I use the sum formula to figure it out.

Answer 4

sin^2 + cos^2 = 1

that's my fav one