Geometry and Trigonometry

Question 1

Pythagorean Theorem

Answer 1

a² + b² = c²,

where c is the hypotenuse

Question 2

Pythagorean Triples

Answer 2

• 3, 4, 5
• (6, 8, 10)
• 5, 12, 13
• 8, 15, 17
• 7, 24, 25

Question 3

Triangle Inequality Theorem =

Answer 3

Sum of any two sides of a triangle ≥ Length of third side

Question 4

Quadrilaterals

(note: height is perpendicular to base)

Answer 4

Question 5

Angle Sum (where 𝑛 =number of sides)

interior angles =

Answer 5

interior angles = (𝑛 − 2)(180°)

Question 6

Angle Sum (where 𝑛 =number of sides)

exterior angles =

Answer 6

(𝑛)(360°) for all polygons

Question 7

𝑠𝑖𝑛𝑒 =

Answer 7

Question 8

𝑐𝑜𝑠𝑖𝑛 =

Answer 8

Question 9

𝑡𝑎𝑛𝑔𝑒𝑛𝑡 =

Answer 9

Question 10

Complementary Angles

Answer 10

The sine of any angle equals the cosine of its complement and vice versa

Question 11

𝑠𝑖𝑛(θ) =

Answer 11

𝑐𝑜𝑠(90 − θ)

Question 12

𝑐𝑜𝑠(θ) =

Answer 12

𝑠𝑖𝑛(90 − θ)

Question 13

Degrees to Radians:

Answer 13

Question 14

Radians to Degrees:

Answer 14

Question 15

Arc:

(θ is the measure of central angle)

Answer 15

Question 16

Sector:

(θ is the measure of central angle)

Answer 16

Question 17

Circle Equation

Answer 17

(𝑥 − ℎ)² + (𝑦 − 𝑘)² = 𝑟²

(ℎ, 𝑘) = circle center coordinates

𝑟 = radius of the circle

Question 18

𝑉𝑜𝑙𝑢𝑚𝑒_{𝐶𝑦𝑙𝑖𝑛𝑑𝑒r} =

Answer 18

π𝑟² ℎ

Question 19

𝑉𝑜𝑙𝑢𝑚𝑒_{𝑆𝑝ℎ𝑒𝑟𝑒} =

Answer 19

Question 20

𝑉𝑜𝑙𝑢𝑚𝑒_Cone

Answer 20

Question 21

𝑉𝑜𝑙𝑢𝑚𝑒_{𝑃𝑦𝑟𝑎𝑚𝑖d}

Answer 21

Question 22

𝑉𝑜𝑙𝑢𝑚𝑒_Box

Answer 22

𝑙𝑤ℎ

Question 23

Surface Area_Cylinder

Answer 23

2π𝑟² + 2π𝑟ℎ