1. Revision
Find the exact values of the following
Use the table you formed or the triangles
/3
60º
sin /3 2
sin /2 1
30º
/6
cos /6 3
tan /4 2 1
cos /4
45º 1
/4

2. Sin ,cos and tan of angles of all sizes in degrees and radian measure
Sin x + + x - -
Cos x + + x - -
Tan x + + x - -
/  / 

3. Positive and negative angles
Angles measured in a clockwise direction are positive
300 º
-60 º
Angles
Angles measured in an anti-clockwise direction are negative
-60 º = 300º

4. Where functions are positive
By looking at the graphs we find in which quadrant the sin ,cos and tan functions are positive and negative
This is summarised in the following table
Where functions are positive
2nd quad
1st quad
ALL
SIN
TAN
COS
4th quad
3rd quad

5. 1 180 + 30  +/6 360-30 2- /6 30º /6 180-30 - /6 -1 =sin30
or sin 5/6
= sin ( - 5/6)
= sin /6
sin 150 =
sin ( )
= - sin (7/6 - )
sin 210 = -
sin ( 210 – 180)
= - sin 30
or sin 7/6
= - sin /6
sin 330 = - sin( 360 –330 ) = - sin 30
or sin 11/6 = sin (2 -11/6) = - sin /6

6. acute 180 - Angle Angle - 180 360 - angle
By looking at the symmetry of the graphs we see that the sines cosines and tangents of all angles can be expressed in terms of the acute angle in the first quadrant , called the related acute angle
See handout
To find the acute angle we use the following diagram
2nd quad
1st quad
acute
180 - Angle
Angle - 180
360 - angle
4th quad
3rd quad

7. Express the cosines of the following angles as cosines of related acute angles
=coc /6
Cos( 2 -11 /6)

8. Express the tangents of the following angles as tangents of related acute angles

9. To find the exact value of trig functions using degrees or radians
Allocate the positive or negative sign depending on the quadrant the angle is in
Express angle as an acute angle
Find it’s exact value using the triangles
and
ALL
SIN
180 - Angle
acute
Angle - 180
360 - angle
COS
TAN

10. Ex 2 p 48 MIA
Do ex 4E on heineman hand out
example
Find the exact value of sin 315 º
4th quad neg
Sin 315 º
= - sin ( ) º
45º
= - sin 45 º
Express as an acute angle 2
= - 1/ 2 1
= - 2/2
45º 1