Trigonometric Identities C3

Question 1

sec(x)

Answer 1

1/[cos x]

Question 2

cosec (x)

Question 3

cot x

Answer 3

1/[tan x]

Question 4

Draw graph of sec x

Answer 4

goes from 1 –> infinity

Question 5

Draw graph of cosec x

Answer 5

Same as graph of sec x but (1 to inf, -inf to -1 to -inf, inf to 1 to inf..) but asymptote at x = 0, x = 180, with y=1 at x = 90

Question 6

Draw graph of cot x

Answer 6

Vertical asymptotes at x = 180n (where sin x = 0), and repeats itself every 180 degrees.

Question 7

Identity linking sin, cos

Question 8

Identity linking tan, sec

Question 9

Identity linking cot, cosec

Answer 9

1 + cot²x = cosec²x

Question 10

Sketch arcsin(x).

What is the domain and range

Answer 10

• 1 ≤ x ≤ 1
• pi/2 ≤ arcsin x ≤ pi/2

Question 11

Sketch arccos(x)

Domain?

Range?

Answer 11

-1 ≤ x ≤ 1

0 ≤ arccos x ≤ pi

Question 12

Sketch arctan(x)

Domain ?

Range?

Answer 12

x e R

-pi/2 ≤ arctan x ≤ pi/2

Question 13

sin(A±B)

Answer 13

sin A cos B ± cos

Question 14

cos(A±B)

Question 15

tan(A+B)

Answer 15

[tan A ± tan B]/[1 ∓ tan A tan B]

Question 16

sin 2A

Answer 16

sin 2A = 2 sin A cos A

Question 17

cos 2A

Answer 17

cos 2A = cos²A - sin²A

= 2cos ²A - 1

= 1 - 2sin²A

Question 18

tan 2A

Question 19

sin P + sin Q

Answer 19

2 sin[(P±Q)/2] cos [(P∓Q)/2]

Question 20

cos P + cos Q

Answer 20

2cos[(P+Q)/2]cos[(P-Q)/2]

Question 21

cos P - cos Q

Answer 21

-2sin[(P+Q)/2]sin[(P-Q)/2]

Question 22

2 sin A cos B

Answer 22

sin[A+B] cos[A-B]

Question 23

How would you convert these products into sums?

2 sin A cos B

2 cos A sin B

2 cos A cos B

2 sin A sin B

Answer 23

USE FACTOR FORMULA BUT REDEFINE VARIABLES SO THE ‘Product side’ is the neat variables.