Math Studies Extra Credit - Geometry and Trigonometry

Finding the Slope of a Line

• Rise / Run
• y/x, vertical/horizontal
• The gradient formula
• y2 - y1 / x2 - x1
• Parallel lines
• When given an equation and another line parallel, the slopes are the same. (ex: m of 3 makes the parallel line of 3
• Perpendicular lines
• when given an equation and another line perpendicular, the slope is the reciprocal (ex: m of 3 makes the perpendicular line -1/3)
• does a point lie on a line?
• substitute the coordinates into x and y and see if the = is true.

Finding Area, Perimeter and Circumfrence

• area & circumfrence of circle
• areas of composite shapes (two shapes together)
• half circle + rectangle (basketball court)
• find the radius of semi-circle (2πr / 2)
• add circumfrence with perimeter of rectangle (add all sides together)
• 

Volume

Finding Midpoint & Distance

Pythagorean Theorem & Trig Ratios

• labelling right angles triangles (opp, hyp, adj)
• SOH CAH TOA
• finding sides (sinx)
• finding angles (sin-1x)

Angle of Elevation and Angle of Depression

Law of Cosines

• Finding sides
• Finding angles
• the Ambiguous case
• ​​​​​​​side 2 > side 1 -> 1 triangle
• side 2 = height -> 1 right triangle
• side 2 < height -> 0 triangles
• side 2 > height > side 1 -> 2 triangles

Law of Sines and the Area of a Triangle