Trig Equation Grade 10
2
+
Cos2T
Cos2T
2T
2T
Reference angle
=
=
=
=
=
1.5
-0.5
arc-cos(-0.5)
120 degrees
60 degrees
=
180 – 60 degrees
A reference angle for a given angle in standard position is the positive acute angle formed by the
x-axis and the terminal side of the given angle.
Cos2T is -ve and so solutions are in the second and third quadrants. Since we have Cos(2T) the
function repeats every 180 degrees and there will be 4 solutions. See the graph on the next page
Q2:
2T
2T
T
=
=
=
180 - 60
120
60
+
+
+
360k
360k
180k
where k iamo Z
where k iamo Z
where k iamo Z
===>
Solutions 0<=T<=360: 60; 60 + 180 = 240
Checks: cos(2x60) = cos(120) = -0.5; Cos(2x240) = cos(480)
[=cos(120)] = -0.5
Q3:
2T
2T
T
=
=
=
180 + 60
240
120
+
+
+
360k
360k
180k
where k iamo Z
where k iamo Z
where k iamo Z
Solutions 0<=T<=360: 120; 120 + 180 = 300
Checks: cos(2x120) = cos(240) = -0.5; Cos(2x300) = cos(600) [=cos(240)] = -0.5
===>