Solving Trig Equations
UNIT CIRCLE APPROACH TO TRIGONOMETRIC
FUNCTIONS
Learn how to determine the values of sines and cosines of angles.
Associating these angles with others in different quadrants of the
trigonometric circle.
Establish the relationship between the trigonometric ratios on the
right angle triangle
30°
45°
60°
120°
135°
150°
sin
1/2
0.71
0.87
0.87
0.71
1/2
cos
0.87
0.71
1/2
-1/2
-0.71
-0.87
Unit Circle. Forming Trig Graphs
http://www.analyzemath.com/unitcircle/unitcircle.html
The Graphs of
Sin, Cos and Tan
The graphs show the value of
sinø, cosø and tanø against ø
(ø represents an angle).
From the sin graph we can see
that sinø = 0 when ø = 0
degrees, 180 degrees and 360
degrees.
Plot on the circle the extremities of some different arcs.
30°,
, 240° and
.
The unit circle and its coordinates
Combine the coordinates of the plotted points and the angles on the graph.
90° (or p/2 rad) is related to the point (0, 1) so, cosine of 90° is equal to zero
and sine of 90° is equals to one;
the concept of trigonometric "cycle" instead of just "circle" shows that we can
obtain an infinite number of angles greater than 360°;
The measurement of the height can be found by using the Pythagorean
theorem and the same triangle can be used to find sine and cosine of 60°.
45 and 60 degrees
sin 450  sin

4

1
2

1
cos 45 cos 
4
2
0
tan 45  tan
0
1
√2

4
1
,45
0

4
1
sin 30 0  sin

6


1
2
3
6
2

1
tan 30 0  tan

6
3
cos 30 0  cos


3
3
2

1
cos 60 0  cos

3
2
sin 60 0  sin
tan 60 0  tan

3

6
,30 0


√3

3
3
1
2
,600

Unit circle and trig graph (All Stations To Crew)
http://www.youtube.com/watch?v=7CcxpBhdYFQ

How to solve sin = +ve value

http://www.youtube.com/watch?v=ZYiIqfErCBA

How to solve sin = -ve value

http://www.youtube.com/watch?v=ijIw4dFN89w&feature=related

How to solve tan = -ve value

http://www.youtube.com/watch?v=ZqItZlf9UX0&feature=related

How to solve 2 cos x – 1 = 0

http://www.youtube.com/watch?v=IE0FxGegdMg&feature=related


Solving sin 2σ = ½
What are trig graphs for?
http://www.youtube.com/watch?v=FUMpGuLIQ5M&feature=related
Unit circle and trig graph (All Stations To Crew)
S
A
T
C
Practice exercises
Theta Mathematics
page 254 exercise 24.4

Rearranging Simple Trig