Fundamental Identities Set 1

Question 1

Pythagorean Identity: sin and cos

Answer 1

sin2θ+cos2θ=1

Question 2

Pythagorean Identity: tan

Answer 2

1+tan2θ=sec2θ

(notice the similarity to cot identity… tan is to sec, bc sin/cos and 1/cos)

Question 3

Pythagorean Identity: cot

Answer 3

1+cot2θ=csc2θ

(notice the similarity to tan identity… cot is to csc, bc cos/sin and 1/sin)

Question 4

Even/Odd Identity:
sin(-u), csc(-u), tan(-u), cot(-u)

Answer 4

-sinu
-cscu
-tanu
-cotu

ALL ODD FUNCTIONS

Only cos and its reciprocal, sec, are even (and -u just turns into the originial cosu and secu). The rest (sin, tan, and their reciprocals are ODD and turn NEG)

Question 5

Even/Odd Identity:
cos(-u), sec(-u)

Answer 5

cosu
secu

BOTH EVEN FUNCTIONS

Only cos and its reciprocal, sec, are even (and -u just turns into the originial cosu and secu).

Question 6

Reciprocal vs Cofunction

Answer 6

reciprocal: sin and csc
cofunction: cos and sin

Question 7

Cofunction Identities:

Answer 7

sin(π/2 - u) = cosu
cos(π/2 - u) = sinu
tan(π/2 - u) = cotu
cot(π/2 - u) = tanu
sec(π/2 - u) = cscu
csc(π/2 - u) = secu

remember, it’s sin/cos, tan/cot, sec/csc whatever, copy+paste formula