CHAPTER 17. TRIGONOMETRY 17.3
Reduction Formula EMBDD
Any trigonometric function whose argument is 90 ◦±θ; 180 ◦±θ; 270 ◦±θ and 360 ◦±θ (hence−θ) can
be written simply in terms of θ. For example, you mayhave noticed that the cosine graph is identical
to the sine graph exceptfor a phase shift of 90 ◦. From this we may expect that sin(90◦+ θ) = cos θ.
Function Values of 180 ◦± θ
Activity: Reduction Formulae forFunction Values of 180 ◦±θ
- Function Values of (180◦− θ)
(a) In the figure P and P�lie on the cir-
cle with radius 2. OP makes an angle
θ = 30◦with the x-axis. P thus has coor-
dinates (√
3;1). If P�is the reflection of
P about the y-axis (or the line x = 0), use
symmetry to write downthe coordinates
of P�.(b) Write down valuesfor sin θ, cos θ and
tan θ.(c) Using the coordinates for P� deter-
mine sin(180◦− θ), cos(180◦− θ) and
tan(180◦− θ).�P0 xyθ�
θP� 180 ◦− θ
22(d) From your results tryand determine a relationship between the function values
of (180◦− θ) and θ.- Function values of (180◦+ θ)
(a) In the figure P and P�lie on the cir-
cle with radius 2. OP makes an angle
θ = 30◦with the x-axis. P thus has coor-
dinates (√
3;1). P�is the inversion of P
through the origin (reflection about both
the x- and y-axes) and lies at an angle of
180 ◦+ θ with the x-axis. Write down the
coordinates of P�.(b) Using the coordinates for P� deter-
mine sin(180◦+ θ), cos(180◦+ θ) and
tan(180◦+ θ).(c) From your results tryand determine a re-
lationship between the function values of
(180◦+ θ) and θ.�P0 xyθ�θ180 ◦+ θP�22