Trig Identities

Question 1

tanθ

Answer 1

sinθ / cosθ

Question 2

cotθ

Answer 2

cosθ / sinθ

Question 3

sin^2 + cos^2

Answer 3

1

Question 4

sec^2

Answer 4

tan^2 + 1

Question 5

cosec^2

Answer 5

cot^2 + 1

Question 6

Cosine rule

Answer 6

a^2 = b^2 + c^2 -2bcCosA

Question 7

Sine rule

Answer 7

a/SinA = b/SinB = c/SinC

Question 8

Area of a triangle

Answer 8

(1/2)abSinC

Question 9

Describe a sec(x) graph

Answer 9

The little loops, with a width of 180 degrees, the first loop is centred over 0 degrees

Question 10

Describe a cosec(x) graph

Answer 10

The little loops, with a width of 180 degrees, every 180 degrees, starting centred over 90 degrees

Question 11

Describe a cot(x) graph

Answer 11

Diagonal curves from top left to bottom right, with a width of 180 degrees, every 180 degrees

Question 12

Describe an arcsin(x) graph

Answer 12

Curve from bottom left to top right.
x axis goes from -1 to 1
y axis goes from minus half pi to half pi

Question 13

Describe a arccos(x) graph

Answer 13

Curve from top left to bottom right.
x axis goes from -1 to 1
y axis goes from 0 to pi

Question 14

Describe a arctan(x) graph

Answer 14

Curve from bottom left to top right.
x axis goes from -infinity to infinity
y axis goes from minus half pi to half pi

Question 15

sin2A

Answer 15

2sinAcosA

Question 16

cos2A (3 identities)

Answer 16

cos^2(A) - sin^2(A)
2cos^2(A) - 1
1 - 2sin^2(A)

Question 17

tan2A

Answer 17

(2tanA)/(1-tan^2(A))