1. CAST Diagram – The basics. Rules 1.Always measure from the x-axis 2.Always put a positive value into the calculator to get the required acute angle. The CAST diagram tells us where the trig graphs are positive. Examples 1. 2.

2. tanѲ = 3 C T AS In degrees in the range 0 to 360

3. sinѲ = 0.3 In degrees in the range 0 to 360 C T AS

4. tanѲ = -0.95 In degrees in the range 0 to 360 C T AS Always invert trig a positive value to give an acute angle and then use the sign of the value to decide where to plot.

5. cosѲ = -0.5 In exact radians in the range 0 to 2 . Hint, do in degrees and convert after. C T AS

6. sinѲ = + In exact radians in the range 0 to 2 . Hint, do in degrees and convert after. C T AS

7. CAST Song to tune of YMCA CAST graph, plots three trig curves in one I say, CAST graph, show when y’s above none I say, CAST graph, is so brill now come on And just solve the trig equations. To use, make the value a plus Next trig, invert, to provide an acute Angle, that we, must plot in two quadrants And read round the angles from nought Chorus It’s fun to work with the C A S T With a cos in quad 4 and all three in quad 1 Anticlockwise the others go... Repeat chorus then whole song Quadrant 4Quadrant 3 Quadrant 1Quadrant 2 0

8. Aims: To be familiar with the inverse trig functions. To be able to solve trigonometry equations that are equal to a constant. To be able to solve a hidden quadratic involving trig. Trigonometry Lesson 4

9. Recall Trig identities We met these last lesson and you will find, that they come in useful when solving trig equations.

10. Trig Equations Solve The equation C T AS

11. Trig Equations Solve The equation C T AS

12. Trig Equations – Hidden Quadratic Solve The equation Firstly we need to make this an equation only involve one type of trig function and so need to make use of this identity

13. Trig Equations – Hidden Quadratic C T AS C T AS Do Exercise C page 59

14. A Challenge!