Chap. 7 - Trigonometry Flashcards
sine ratio
o/h
cos ration
a/h
tan ratio
o/a
how do you calculate unknown angles using a calculator
put the fraction / number into the inverse of the ratio
e.g sin(theta) = 1/2
theta = sin^-1(1/2)
in terms of linear relationships, how do you calculate the gradient using trigonometry?
tan(theta) = m (the gradient)
what is the angle of inclination in linear relationships
between a line and the positive direction of the x-axis
The angle of elevation is measured
up from the horizontal
The angle of depression is measured
down from the horizontal
true bearings are measured:
clockwise from the northline
to find the answer in a bearings question, the first step (in evie’s brain) is to
MAKE A GRAPH!!!!!!!!
two tips for trig in 3d ARE
- draw a careful diagram with all right angled triangles marked
- top down view can help
sin30 =
1/2
sin 60 =
√3 / 2
cos30
√3 / 2
cos60
1/2
tan30
1 / √3
tan60
√3
angles in the 1st quadrant are always:
acute
sin(theta) = cos…
(90 - theta)
angles in the 2nd quadrant are always
obtuse
cos(180° − θ) =
−cos θ
sin(180° − θ) =
sin θ
tan(180° − θ) =
−tan θ
the sine rule is
a/sinA = b/sinB = c/sinC
the sine rule is used when
when we are given either
a) two angles and one side, or b) two sides and a non-included angle
the ambiguoes case exists when
*you’re using the sine rule
*you’re finding an angle
*the given angle is acute
*the sum of the two possible answers does not exceed 180°
use the cosine rule when
*given 3 sides of a triangle
*given 2 sides and an included angle
side a and b are adjacent to
angle C
area of a triangle is given by:
A=1/2absinC
to complete area of a triangle you need
two sides and a given angle
what is the related angle
the angle between the x axis and the hypotenuse of the triangle
explain the ALL STATIONS TO CENTRAL nemonic
A = all positive
S = only sin is positive
T = only tan is positive
c = only cos is positive
what does the related angle do?
it helps you find sin, cos and tan theta for any size
how do you evaluate angles of any magnitude using the related angle?
- determine which quadrant the new angle is in
- determine the size of the related angle using the quadrant location
- establish your answer as positive or negative
- using special triangles, put the answer in integer form if possible, (e.g -tan45 = -1)
ASK MR DELHORY ABOUT BOUNDARY ANGLES!!!!!!!
