Trigonometry

Question 1

Arc Length

Answer 1

θr

Question 2

Sector Area

Answer 2

1/2 r^2 θ

Question 3

Segment Area

Answer 3

1/2 r^2 (θ - sin θ)

Question 4

tan θ equation

Answer 4

sin θ/cos θ

Question 5

cot θ

Answer 5

cos θ/sin θ

Question 6

Trig equations which = 1

Answer 6

cos^2 θ + sin^2 θ = 1
cot^2 θ - cosec^2 θ = 1
tan^2 θ - sec^2 θ = 1

Question 7

sin 2θ

Answer 7

2 sin θ cos θ

Question 8

cos 2θ

Answer 8

cos^2 θ - sin^2 θ

Question 9

tan 2θ

Answer 9

(2tan θ) / (1 - tan^2 θ)

Question 10

sin (a + b)

Answer 10

sin a cos b + cos a sin b

Question 11

sin (a - b)

Answer 11

sin a cos b - cos a sin b

Question 12

cos (a + b)

Answer 12

cos a cos b - sin a sin b

Question 13

cos (a - b)

Answer 13

cos a cos b + sin a sin b

Question 14

tan (a + b)

Answer 14

(tan a + tan b) / (1 - tan a tan b)

Question 15

tan (a - b)

Answer 15

(tan a - tan b) / (1 + tan a tan b)

Question 16

Small Angle tan θ

Answer 16

tan θ ≈ θ

Question 17

Small Angle sin θ

Answer 17

sin θ ≈ θ

Question 18

Small Angle cos θ

Answer 18

cos θ ≈ 1 - (θ^2) / 2