Chap 15 - bearings, scale drawing, trig Flashcards
rules for bearings
-clockwise from north
-3 figure ans
-be careful of the “form” - highlight it
-co interior angles - a + b = 180
how to do scale drawing
-make units the same before converting to ratio
-if drawing is to scale, can measure drawing
how to find θ for right angled triangles
-SOH CAH TOA
sin θ = O/ H
cos θ = A/ H
tan θ = O/ A
-O is side opposite θ
-H is longest side
what does it mean to give ans in exact form
give ans in √
how to find angle of elevation/ depression
-angle directly above the line is angle of elevation
-angle directly below the line is angle of depression
-Be careful with the angles
Pythagoras theorem
a^2 + b^2 = c^2
properties of sine wave
-limits: 1, -1
-start: 0
-360 cycle
properties of cosine wave
-limits: 1, -1
-start: 1
-360 cycle
properties of tan wave
-limits: none
-start: 0
-180 cycle
functions for sine, cosine, tan
1) sine
x< 180 (x = +) __ sin x = sin (180 - x)
x> 180 (x = -) __ x - 180 = y , sin x = sin (360- y)
2) cosine
x< 90/ x> 270 (x = +) __ cos x = -cos (180 - x)
90< x< 270 (x = -) __ cos x = cos (360 - x)
3) tan
tan x = tan (180 + x)
sine rule
A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
a b
——– = ——–
sin A sin B
-cross multiply
-2 sides, 1 angle/ 1 side, 2 angles
cosine rule
A, B, C - angle
a, b, c - side (side has to be opposite same letter angle)
-c^2 = a^2 + b^2 - 2ab cos C
-cos C = a^2 + b^2 - c^2
————————-
2ab
-3 sides/ 2 sides, 1 angle
area of a right angled triangle
1/2 x base x height
area of non right angle triangle
1/2 x ab sincC
how to find area of shapes
make as many right angled triangle as possible
