Trigonometry Flashcards
What is the formula for the Cosine Rule?
a^2=b^2 + c^2 - 2bc cosA
For ease with using equation, label the INCLUDED angle A and this will mean the unknown side is a.
This can be rearranged to find a value for cosA.
When do you use the Sine Rule or Cosine Rule in triangles to find missing sides/angles?
When the triangle is not a right angle triangle
When do you use Sin, Cos, or Tan in triangles to find missing sides/angles?
When the triangle is a right angle triangle
What do you have to remember about the Sine Rule?
It is all about opposites. I.E. if there is a triangle that has an unknown angle opposite to a known side/an unknown side opposite to a known angle and there’s also a known side opposite a known angle- we can use Sine Rule.
Also make sure to label your triangle using A, B, C for the angles and a, b, c for the corresponding sides.
What do you have to remember about using the Cosine Rule?
It’s all about being included. We use this formula when we have an angle INBETWEEN two known sides (this angle is called the INCLUDED angle) and we use this to find the unknown side opposite the included angle.
Also make sure to label your triangle using A, B, C for the angles and a, b, c for the corresponding sides. Your INCLUDED angle tells you which sides are b and c and the opposite side to the INCLUDED angle is just a.
What is the formula for the Sine Rule for finding any one of the three sides of a triangle?
a /sinA = b/sinB = c/sinC
You might use the As and Bs but not the Cs. You only need to use two of them.
What is the formula for the Sine Rule for finding any one of the three angles in a triangle?
sinA/a = sinB/b = sinC/c
You might use the As and Bs but not the Cs. You only need to use two of them.
How is the formula for Cosine Rule rearranged to find the value of an angle in a non-right angle triangle?
cosA= b^2 + c^2 -a^2/2bc
For ease, label the missing angle A.
The a^2 will be the side opposite the missing angle.
What do you have to do if you’re trying to find an angle but you have a value of Sin (x), Cos (x), or Tan (x)?
You do the inverse (Sin^-1, Cos^-1, Tan^-1) to find the value for the angle
How do we find the area of a triangle without knowing the height of the triangle (using Sin)?
We use the equation:
Area= 1/2ab sinC
Label the known angle C and the two sides that INCLUDE (surround) the angle C are a and b.
It can be done using any two sides and the angle between (angle is C and the two sides are a and b)- even if you labelled another side a and another side b, for this equation the sides that surround the INCLUDED angle are a and b.
