Everything Maths Grade 11

CHAPTER 17. TRIGONOMETRY 17.3

Intercepts

For functions of the form, y = tan(θ + p), the details of calculating the intercepts with the y axis are
given.

The y-intercept is calculated as follows: set θ = 0◦

y = tan(θ + p)

yint = tan(p)

Asymptotes

The graph of tan(θ + p) has asymptotes because as θ + p approaches 90 ◦, tan(θ + p) approaches
infinity. Thus, there is no defined value of the function at the asymptotevalues.

Exercise 17 - 7

Using your knowledge of the effects of p and k draw a rough sketch ofthe following graphs without a
table of values.

1. y = sin3x


2. y =−cos2x


3. y = tan^12 x


4. y = sin(x− 45 ◦)


5. y = cos(x + 45◦)


6. y = tan(x− 45 ◦)


7. y = 2sin2x


8. y = sin(x + 30◦) + 1

More practice video solutions or help at http://www.everythingmaths.co.za

(1.) 0148 (2.) 0149 (3.) 014a (4.) 014b (5.) 014c (6.) 014d

(7.) 014e (8.) 014f

17.3 Trigonometric Identities

Deriving Values of Trigonometric Functions

for 30

◦

, 45

◦

and 60

◦

EMBDA

Keeping in mind that trigonometric functions apply only to right-angled triangles, we can derive values
of trigonometric functions for 30 ◦, 45 ◦and 60 ◦. We shall start with 45 ◦as this is the easiest.