What is cos(30-theta)?

3 Answers

1. cos(30 – t)

   The cosine subtraction formula goes as follows:

   cos(a – b) = cos(a)cos(b) + sin(a)sin(b)

   So if we wanted cos(30 – t), we would get

   cos(30 – t) = cos(30) cos(t) + sin(30)sin(t)

   Cosine of 30 degrees is sqrt(3)/2.

   Sine of 30 degrees is 1/2.

   cos(30 – t) = [sqrt(3)/2] cos(t) + (1/2)sin(t)

   If we wanted to put this under one fraction, we would get

   cos(30 – t) = [sqrt(3) cos(t) + sin(t)]/2

2. We need to know what Theta is.

   However your teacher probably wants you to use the trig identities for adding and subtracting angles

   cos (A – B) = cos(A)Cos(B) + sin(A)sin(B)

   cos (30 – Y) = cos(30)cos(Y) – sin(30)sin(Y) where Y is Theta

3. cos(A – B) = cos(A)*cos(B) + sin(A)*sin(B)

   cos(30 – t) = cos(30)*cos(t) + sin(30)*sin(t) = √3/2*cos(t) + sin(t)/2