Math- Trig Identities

Question 1

derivative of acrtanx

Answer 1

1/1 +x^2

Question 2

Unit Circle ratios

Answer 2

Adjacent length = x length
Opposite length= y length
Hypotenuse length = 1 (unit cirle)

Sin x = y/1 = y

Cos x = x/1 = x

Tan x = y/x

Question 3

Pythagorean identities (3)

Answer 3

Sin^2 + cos^2 = 1

Tan^2 + 1 = sec^2

1 + cot^2 = csc^2

Question 4

Rework: sin^2 + cos^2 = 1

Answer 4

Cos^2 = 1- sin^2

Sin^2 = 1- cos^2

Cos^2 and Sin^2 interchangeable in this form

Question 5

Rework: tan^2 + 1 = sec^2

Answer 5

Sec^2 - tan^2 = 1

tan^2 = sec^ 2 - 1

Sec = 1/cos

Tan= sin/cos

Question 6

Rework: 1 + cot^2 = csc^2

Answer 6

Cot^2 = csc^2 - 1

Csc^2 - cot^2 = 1

Csc = 1/sin

Cot= cos/sin

Question 7

Unit circle: 0 or 2pi

Answer 7

Cos = 1

Sin= 0

Tan = cos/sin = 1/0 = undefined?

Question 8

Unit circle: pi/6

Answer 8

Cos or x: sqrt(3)/2

Sin or y: 1/2

Tan: (1/2)/(sqrt(3)/2)= 1/sqrt(3)

Question 9

Unit circle: pi/4

Answer 9

Cos or x: sqrt(2)/2 or 1/sqrt(2

Sin or y: sqrt(2)/2 or 1/sqrt(2

Tan: 1

Question 10

Unit circle: pi/3

Answer 10

Cos or x: 1/2

Sin or y: sqrt(3)/2

Tan: sqrt(3)/2 / (1/2) = sqrt(3)

Question 11

Unit circle: pi/2

Answer 11

Cos or x: 0

Sin or y: 1

Tan: 0/1 = 0

Question 12

Sin 2x

Answer 12

2 sin cos

Question 13

Cos 2x

Answer 13

Cos ^2 - Sin^2

Question 14

Sin^2 x

Answer 14

1 - cos2x / 2

Question 15

Cos^2 x

Answer 15

1+ cos2x / 2