Trigonometry

Question 1

How convert from degrees to radians?

Answer 1

Divide by 360, times by 2π

Question 2

What are the small angle approximations?

Answer 2

Sin θ = θ
Cos θ = 1- θ^2/2
Tan θ = θ

Question 3

Definition of tangent (trig. )?

Answer 3

Sin x/Cos x = Tan x

Question 4

How do you find more solutions for Sin x, Cos x and Tan x?

Answer 4

Sin x: sin(180-x) then add 360 to each solution within interval
Cos x: cos(360-x) then add 360 to each solution within interval
Tan x: tan x then add 180 to answer until interval fulfilled

Question 5

What are the inverse trig functions?

Answer 5

Cosec x = 1/sin x
Sec x = 1/cos x
Cot x = 1/tan x = cos x/sin x

Question 6

How do sin x and cos x relate?

Answer 6

Sin x = Cos (90 - x), Cos x = sin (90 - x)

Question 7

Sin^2 x + Cos^2 x =?

Answer 7

1

Question 8

1+ tan^2 x =?

Answer 8

Sec^2 x

Question 9

1 + Cot^2 x =?

Answer 9

Cosec^2 x

Question 10

Sin (A+B) =?

Answer 10

Sin A Cos B + Sin B Cos A

Question 11

Cos (A+B)

Answer 11

Cos A Cos B - Sin A Sin B

Question 12

Tan (A+B) =?

Answer 12

(Tan A + Tan B) / 1 - Tan A Tan B

Question 13

Sin 2x =

Answer 13

2sin x cos x

Question 14

Cos 2x =
(All 3 versions)

Answer 14

Cos^2 x - Sin^2 x
2Cos^2x - 1
1 - 2Sin^2x

Question 15

Tan 2x =?

Answer 15

2Tan x / (1 - Tan x)

Question 16

Sin^2 x =?
(Rearranged double angle)

Answer 16

1/2 -1/2 Cos 2x

Question 17

Cos^2 x =?

Answer 17

1/2 + 1/2 Cos 2x
(Rearranged double angle)

Question 18

What is the harmonic identity?
(R Cos (x+a))

Answer 18

If R Cos α = a, R Sin α = b
R = rt. a^2 + b^2
Tan α = b/a