Question

(1 point) For each trigonometric expression A,B,C,D, E, choose the expression from 1,2,3,4,5 that completes a fundamental identity. Enter the appropriate letter (A,B,C,D, or E) in each blank.

Answer 1

Explanation:

I would recommend looking up the magic trig hexagon, it has all of these identities and more within it.

1 - this corresponds with C as sin^2(x)+cos^2(x)=1

1-cos^2(x) - this corresponds with A, using the identity from number 1, we can rewrite it in the form sin^2(x)=1-cos^2(x)

cot(x) - for this it is important to know that cotangent is the inverse of tangent. Since tan(x)=sin(x)/cos(x), cot=cos(x)/sin(x) which is B.

sec^2(x) - much like the cos and sin pythagorean identity, sec and tan are related. sec^2(x)=tan^2(x)+1 which is answer choice E.

tan(x) - this is sin(x)/cos(x), choice D.