Core 4 - Trigonometry + DA

Question 1

What are the three double angles for cos(2x)

Answer 1

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

Question 2

Give the addition formula for sin(a+b)

Answer 2

=sinAcosB + cosAsinB

Question 3

Give the addition formula for sin(a-b)

Answer 3

=sinAcosB - cosAsinB

Question 4

Give the addition formula for cos(a-b)

Answer 4

cosAcosB + sinAsinB

Question 5

Give the addition formula for cos(a+b)

Answer 5

cosAcosB - sinAsinB

Question 6

Give the addition formula for tan(a+b)

Answer 6

(tanA+tanB)/(1-tanAtanB)

Question 7

Give the addition formula for tan(a-b)

Answer 7

(tanA-tanB)/(1+tanAtanB)

Question 8

In which quadrants are sin cos and tan positive?

Answer 8

Acute - all +ve
Obtuse - sin
Reflex 1 - tan
Reflex 2 - cos

Question 9

When solving an equation involving two trig functions, and you can factorise, what must you do?

Use the example 3sin2x = sinx

Answer 9

DO NOT DIVIDE THROUGH 
If sinx =0, you cannot divide through by this as it gives an infinite value.
2sinxcosx=(sinx)/3
sinx(2cosx-1/3)=0
therefore
sinx=0
2cosx=1/3

Question 10

What is the (not required but useful) identity for (cos(a))(cos(b))

Answer 10

1/2(cos(a+b)+(cos((a-b))