9. Trigonometric Ratios

Question 1

Sine rule

Answer 1

SinA/a = SinB/b = SinC/c

Or the inverse

Question 2

Cosine rule

Answer 2

a^2 = b^2 + c^2 - 2bcCosA

Question 3

Rearranged cosine rule

Answer 3

Cos A = a^2 - b^2 - c^2
—————————
-2bc

Question 4

What to do when using sine rule

Answer 4

Check whether the obtuse angle is the one you need (ambiguous case)

Question 5

Area of a triangle

Answer 5

1/2 a b SinC

Where C is the angle between sides a and b

Question 6

Where is the largest angle in a triangle?

Answer 6

Opposite the largest side

Question 7

Sine graph

Answer 7

Repeats every 360 (starting at -360, 0, 360 etc)

Starts at 0, 1 at 90, 0 at 180, -1 at 270, 0 at 360

Question 8

Cosine graph

Answer 8

Repeats every 360 (starting at -360, 0, 360 etc)

Starts at 1, 0 at 90, -1 at 180, 0 at 270, 1 at 360

Question 9

Tan graph

Answer 9

Repeats every 180 (starts at -270, -90, 90, 270 etc)
Asymptotes at those x values
Goes up to infinity and down to negative infinity
Almost vertical at those points, curves through 0 between