Trigonometry

Question 1

tan(θ)

Answer 1

sin(θ)/cos(θ)

Question 2

sec(θ)

Answer 2

1/cos(θ)

Question 3

cot(θ)

Answer 3

1/tan(θ) or cos(θ)/sin(θ)

Question 4

cosec(θ)

Answer 4

1/sin(θ)

Question 5

1

Answer 5

1=sin^2(θ) + cos^2(θ)

Question 6

sec^2(θ)

Answer 6

sec^2(θ)= 1 + tan^2(θ)

Question 7

cosec^2(θ)

Answer 7

cosec^2(θ)= 1 + cot^2(θ)

Question 8

cos(2A)

Answer 8

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

Question 9

sin(2A)

Answer 9

2sin(A)cos(A)

Question 10

tan(2A)

Answer 10

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

Question 11

sin(A+B)

Answer 11

sin(A)cos(B)+sin(B)cos(A)

Question 12

sin(A-B)

Answer 12

sin(A)cos(B)-sin(B)cos(A)

Question 13

cos(A+B)

Answer 13

cos(A)cos(B)-sin(A)sin(B)

Question 14

cos(A-B)

Answer 14

cos(A)cos(B)+sin(A)sin(B)

Question 15

tan(A+B)

Answer 15

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

Question 16

tan(A-B)

Answer 16

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

Question 17

cos(90-x)

Answer 17

cos(90-x)=sin(x)

Question 18

Rule for exam qs with sin(3x) etc

Answer 18

if have to work out sin(3x) use sin(3x)=sin(2x+x) double angle formula

Question 19

How can you solve cos(50+x)=sin(30+x)

Answer 19

Use double angle formula on each side

Question 20

Area=

Answer 20

0.5absin(c)

Question 21

a^2=

Answer 21

b^2 + c^2 - 2bc cos(a)

Question 22

cos(a)=

Answer 22

(b^2+c^2-a^2) / (2bc)

Question 23

always remeber when using sin(2x) to solve equations to multiply coefficient by 2

Answer 23

Examples: 5sin(2x)=10sin(x)cos(x)

2sin(2x)=4sin(x)cos(x)

Question 24

cos(x)=cos(-x)

Answer 24

-sin(x)=sin(-x)

Question 25

How to prove sin^2(x) + cos^2(x) = 1

Answer 25

use a trianle with sides a b and c
Right angle triangle with x as angle
work out cos (x) and sin (x) in terms of a,b and c. Square each and use to prove by also finding h in terms of a,b and c.

Question 26

How to prove cos(a+b)

Answer 26

Use cos(a-d)
d=-b 
Use cos(-b)=cos(b) and sin(-b)=-sin(b)