Chapter 9 - Trigonometric Ratios

Question 1

What is the cosine rule to find a missing side, if you know two sides and the angle between them?

Answer 1

a^2=

b^2 + c^2 - 2bcCosA

Question 2

What is the cosine rule to find an angle if you know all three sides?

Answer 2

CosA=
b^2 + c^2 - a^2
————————
2bc

Question 3

What is the sine rule used to find the length of a missing side?

Answer 3

a b c
—— = —— = ——
SinA SinB SinC

Question 4

What is the sine rule that is used to find a missing angle?

Answer 4

SinA SinB SinC
—— = —— = ——
a b c

Question 5

If the sine rule sometimes produces 2 possible solutions, how do you find the second possible solution?

Answer 5

Sin• = sin(180 - •)

Question 6

What is the area of any triangle using sine?

Answer 6

1
— ab SinC
2

Question 7

What is the graph of

y= sin• like?

Answer 7

The graph repeats every 360*.

It crosses the x-axis at 0, 180 , 360.

It has a minimum value of -1 and maximum value of 1.

Question 8

What is the graph of

y= Cos• like?

Answer 8

The graph repeats every 360*.

It crosses the x-axis at 90 and 270.

It has a minimum value of -1 and maximum value of 1.

Question 9

What is the graph of

y= tan• like?

Answer 9

The graph repeats every 180*.

It crosses the x-axis at 0, 180, 360.

It has no maximum or minimum value.

It has vertical asymptotes at

x= 90, 270.