Trigonometry

Question 1

4 formulas that require right triangles

Answer 1

sin x = opp / hyp
cos x = adj / hyp
tan x = opp / adj
a² + b² = c²

SOH-CAH-TOA & Phythagorean Theorem

Question 2

2 formulas that do not require right triangles

Answer 2

a² = b² + c² - 2bc cos A
a / sin A = b / sin B = c / sin C

Cosine Law & Sine Law

Question 3

1 formula that works for all triangles (right or non-right)

Answer 3

A + B + C = 180°

Sum of the angles of a triangle

Question 4

Formula to find an angle when you know 3 side lengths and no angles

Answer 4

cos A = (b² + c² - a²) / (2bc)
to find angle A

Cosine Law in reverse

Question 5

Formula to find a side length when you know 2 side lengths in a right triangle

Answer 5

a² + b² = c²

Pythagorean Theorem

Question 6

Formula to find a side length when you know 2 side lengths & the angle between them

Answer 6

a² = b² + c² - 2bc cos A

Cosine Law

Question 7

Formula to find a side length when you know 1 angle & its opposite side length, plus the angle opposite the unknown side

Answer 7

a / sin A = b / sin B = c / sin C

Sine Law

Question 8

Formula to find an angle when you know 1 angle & its opposite side length, plus the side length opposite the unknown angle

Answer 8

sin A / a = sin B / b = sin C / c

Sine Law

Question 9

Formula to find a side length when you know 1 side length and 1 angle in a right triangle

Answer 9

One of…
sin x = opp / hyp
cos x = adj / hyp
tan x = opp / adj

depending on the angle & sides you know

SOH-CAH-TOA

Question 10

Formula to find an angle when you know 2 side lengths in a right triangle

Answer 10

One of…
sin x = opp / hyp
cos x = adj / hyp
tan x = opp / adj

depending on the angle & sides you know

SOH-CAH-TOA

Question 11

When using the Cosine Law to solve for a side length, what last step is always necessary?

Answer 11

Square Root

since if the Cosine Law used is
a² = b² + c² - 2bc cos A
then the side length needed would be a
but this cosine law gives a²

Question 12

When using the Pythagorean Theorem to solve for a side length, what last step is always necessary?

Answer 12

Square Root

since if the Pythagorean Theorem used is
c² = a² + b²
then the side length needed would be c
but this Pythagorean Theorem gives c²

Question 13

When using the Cosine Law to solve for an angle, what last step is always necessary?

Answer 13

Inverse Cosine

since if the Cosine Law used is
cos A = (b² + c² - a²) / (2bc)
then the side length needed would be A
but this cosine law gives cos A

Question 14

When using the Sine Law to solve for an angle, what 2 last steps are always necessary?

Answer 14

Multiplication & Inverse Sine

since if the Sine Law used to find A is
sin A / a = sin B / b
then you would need to
1 – multiply both sides by a giving
sin A = a * sin B / b
2 – then the angle would be A but this formula gives sin A