Algebra 2b U7 L8 Trigonometric Identities
tan²A +1 = sec²A; cotA = -(3√7/7); A = 311.41°
secA = 4/3
sec²A = 16/9
Use the identity tan²A +1 = sec²A
tan²A = sec²A - 1 = 16/9 - 1 = 7/9
cot²A = 1/tan²A = 9/7
We are in the fourth quadrant, so the cotangent is negative.
cotA = -√(9/7) = -3/√7 = -(3√7/7)
tan A = 1/cotA = -√7/3
A = -48.59° = 311.41°
The expression that represents is
The trigonometric equation given to us is
We take the cosine inverse of both sides to obtain,
Recall that, the composition of a function of x and its inverse produces x.
That is or
This implies that,
The correct answer is C.
The domain of a function are the inputs of the function, that is, a function is a relation that assigns to each element in the set A exactly one element in the set B. The set A is the domain (or set of inputs) of the function and the set B contains the range (or set of outputs).Then applying this concept to our function we can write its domain as follows:
1. Domain of validity for :
where k is an integer either positive or negative. That is:
To match this with the choices above, the answer is:
"All real numbers except multiples of "
2. which identity is not used in the proof of the identity :
This identity can proved as follows:
The identity that is not used is as established in the statement above:
"1 +cos squared theta over sin squared theta= csc2theta"
Written in mathematical language as follows: