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

Sin ,cos and tan of angles of all sizes in degrees and radian measure Sin x + + x - - Cos x + + x - - Tan x + + x - - 0 90 180 270 360 0 /2  3/2 2

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

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

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 (180-150) = - 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

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

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

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

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

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 (360-315) º 45º = - sin 45 º Express as an acute angle 2 = - 1/ 2 1 = - 2/2 45º 1