Sine and Cosine

Question 1

How is the Sine rule used for the calculation of sides?

Answer 1

a/SinA = b/SinB = c/SinC

This is used when we have an opposite angle and an opposite side plus a given side or angle opposite to the unkown.

Question 2

How does the Sine rule apply to the calculation of angles?

Answer 2

SinA/a = SinB/b = SinC/c

This is used when we have an opposite angle and an opposite side plus a given side or angle opposite to the unkown.

Question 3

When can the Sine rule be applied?

Answer 3

The Sine rule can be applied when we are given an opposite angle and its opposite side as well as a given side or angle, opposite to the unknown.

Question 4

What format of the Cosine rule is used to calculate the side of a triangle?

Answer 4

a² = b² + c² - 2bc CosA

Other forms of the formula are:
b² = a² + c² - 2ac CosB
c² = a² + b² - 2ab CosC

This can be used to calculate a side when given two sides and an angle in between the two sides.

Question 5

What form of the Cosine rule can be used to calculate the angle of a triangle?

Answer 5

CosA =
b² + c² - a²
_____________
2bc

Other forms of the formula are:
CosB = (a² + c² - b²)/2ac
CosC = (b² + a² - c²)/2ab

This can be used to find the angle of a triangle when given all three of its sides.

Question 6

On what condition can we use the Cosine rule to calculate the side of a triangle?

Answer 6

The Cosine rule can be used to calculate the side of a triangle when given two other sides and and angle in between the two sides.

Question 7

On what condition can we use the Cosine rule to calculate the angle of a triangle?

Answer 7

The Cosine rule can be used to calculate the angle of a triangle on the condition that the three sides of the triangle are given.