BrittneyMay16 said:
I am having some trouble with the trigonometric identities. I can't seem to figure out how to solve the questions.
1. Cos(Theta) = Sin(Theta) / Tan(Theta)
2. Sin(Theta) = Tan(Theta) Cos(Theta)
Can someone please show me how to figure these out ASAP!!!
Let me use x for (theta):
cos x = sin x / tan x
The DEFINITION for tan x is this: tan x = sin x / cos x
What happens if we replace tan x with its equivalent, sin x / cos x?
cos x = sin x / tan x
cos x = sin x / (sin x / cos x)
Now, do the division. Remember that dividing by a fraction is the same as multiplying by the reciprocal. In other words, a / (b / c) = a*(c/b).
cos x = sin x / (sin x / cos x)
becomes
cos x = sin x * (cos x / sin x)
Now, on the right side, do the multiplication:
cos x = (sin x * cos x) / (sin x)
And reduce the fraction:
cos x = cos x
Because we were able to transform the right side so that it looks exactly like the left side, we've shown that this is an identity.
Try the same sort of thing on the second problem.
