Trig Formulae and Trig equations

Question 1

What is the Double Angle Formulae

Answer 1

sin2A = 2sinAcosA
cos2A = 2cos2A - 1
= 1 - 2sin2A
= cos2A – sin2A

Question 2

3cos2x – 5cosx – 2 = 0
what happens when you 
Let p = cosx
p = ?
x = ?
cosx = ?

Answer 2

3p2 – 5p - 2 = 0
(3p + 1)(p -2) = 0
p = cosx = 1/3
x = cos-1( 1/3)
x = 109.5 and 250.5
cosx = 2

Question 3

The exact value of sinx

Answer 3

sinx = 2sin(x/2)cos(x/2)
sinx = 2 (¼ + √(42 - 12) )
sinx = ½ + 2√15)

Question 4

Addition Formulae

Answer 4

sin(A ± B) = sinAcosB cosAsinB
+
-
cos(A ± B) = cosAcosB sinAsinB

Question 5

What do we consider to be the double angle formulae

Answer 5

sin2A and cos2A

Question 6

Formulae for sin (A + B) and cos (A + B)

Answer 6

ssin(A ± B) = sinAcosB cosAsinB
+ = tan (A + B)
- tanA + tanB
cos(A ± B) = cosAcosB sinAsinB 1 - tanA tanB

Question 7

How are the addition formulae appear?/ what does it look like?

Answer 7

(a + β)

Question 8

why is the addition formulae used?

Answer 8

to express the sine and cosine of the sum of two angles in term of sines and cosines of the individual angles