Trig I No Longer Care About for the GRE

Question 1

tan²θ, csc²θ, cot²θ, and sec²θ relationships

Answer 1

1 + tan²θ = sec²θ 1 + cot²θ = csc²θ

Question 2

cotθ = tan(a) What is a?

Answer 2

a = π/2 - θ so cotθ = tan(π/2 - θ)

Question 3

sin(2x)

Answer 3

Double-angle formula: 2sinxcosx

Question 4

cos(2x)

Answer 4

Double-angle formula:

cos²x-sin²x

=2cos²x-1

=1-2sin²x

Question 5

tan(2x)

Answer 5

Double-angle formula: (2tanx) / (1-tan²x)

Question 6

∫ sec²x dx

Answer 6

tanx + C

Question 7

∫ 1/(x²+1) dx

Answer 7

tan⁻¹x + C

Question 8

∫ cscx cotx dx

Answer 8

-cscx + C

Question 9

∫ 1/√(1-x²) dx

Answer 9

sin⁻¹x + C

Question 10

sin²x

Answer 10

Half-angle formula: (1-cos(2x))/2

Question 11

cos²x

Answer 11

Half-angle formula: (1+cos(2x))/2

Question 12

∫dx/(x²+a²)

Answer 12

1/a tan⁻¹(x/a) + C

Question 13

Trig sub for √(a²-x²)

Answer 13

x=asinθ

Question 14

Trig sub for √(a²+x²)

Answer 14

x=atanθ

Question 15

Trig sub for √(x²-a²)

Answer 15

x=asecθ

Question 16

2sinxcosx

Answer 16

Double-angle formula sin(2x)

Question 17

cos²x-sin²x

Answer 17

Double-angle formula

cos(2x)

2cos²x-1

1-2sin²x

Question 18

2cos²x-1

Answer 18

Double-angle formula

cos(2x)

cos²x-sin²x

1-2sin²x

Question 19

1-2sin²x

Answer 19

Double-angle formula

cos(2x)

cos²x-sin²x

2cos²x-1

Question 20

(1-cos(2x))/2

Answer 20

Half-angle formula sin²x

Question 21

(1+cos(2x))/2

Answer 21

Half-angle formula cos²x

Question 22

sin(x+y)

Answer 22

sinx cosy + cosx siny

Question 23

sinx cosy + cosx siny

Answer 23

sin(x+y)

Question 24

sin(x-y)

Answer 24

sinx cosy - cosx siny

Question 25

cos(x+y)

Answer 25

cosx cosy - sinx siny

Question 26

cos(x-y)

Answer 26

cosx cosy + sinx siny

Question 27

sinx cosy - cosx siny

Answer 27

sin(x-y)

Question 28

cosx cosy + sinx siny

Answer 28

cos(x-y)

Question 29

cosx cosy - sinx siny

Answer 29

cos(x+y)

Question 30

cosa cosb

Answer 30

½(cos(a+b)+cos(a-b))

Question 31

sina sinb

Answer 31

½(cos(a-b) - cos(a+b))

Question 32

sina cosb

Answer 32

½(sin(a+b) ± sin(a-b))

Question 33

½(cos(a+b)+cos(a-b))

Answer 33

cosa cosb

Question 34

½(cos(a-b) - cos(a+b))

Answer 34

sina sinb

Question 35

½(sin(a+b) ± sin(a-b))

Answer 35

sina cosb