Page 256-257, Ex. 10.3:
#1, 3 a-b-c-d-h, 4 a-b-e, 7, & 9
[In question 3, when they say "state the corresponding range of y, they mean the range of the outputs or the interval between the minimum and maximum values. Also, for question 7, you may want to draw accurate sketches on graph paper as you will have to rely on those sketches for what is being asked.]
Page 258, Ex. 10.4:
#2, 3, 4, 6 & 7.
Note: In many of the questions you will be required to apply what you already know in new situations. Do not forget the basics and in any circumstance, try something before coming on to the blog and asking a question.
sir for question nine rather than sketching the graphs of tan x and cos x on the same graph can we use a graph plotter(graphamatica) for more accurate results?
ReplyDeleteSir, for questions 3 and four to obtain accurate results should we plot a table of values? If yes shall we make the tables on the graph book?
ReplyDeleteOkay, for question 3 and 4 you don't need a table of values, just use your original graphs and your understanding of transformations and sketch graphs that enable you to know the behaviour, and the mins and maxes (if any) of the graphs. Also, something we have not quite done in class as such, for the tangent function graphs, you should really think about what a vertical stretch or compression would look like and whether that would change any asymptotes.
ReplyDeleteNow for question 7 and 9, as Duaa has asked, no a graph plotter is not a tool I want you to use. The whole point is for you to be able to make accurate sketches (without always having to plot values) based on your understanding of the original sketch. For this, to start with you may need to plot actual points for reference.
ReplyDeleteTry to understand what is being asked of you from the questions. To know roots of certain equations is being related to intersections of function graphs and to know how many intersection within a certain domain will require some accurate plotting. Some of these equations are hard to solve algebraically and the number of solutions are best anticipated graphically.
Please note, I am not against using a graph plotting software, but I need you to know the point behind these graphs and in these cases, you getting a good sense of where they lie YOURSELF is more important. (If you note, question 9 is a Cambridge-based question which certainly won't let you have a graph plotting calculator at your fingertips.)
You may cut paste graphs from your graph book as you see fit!
ReplyDeleteFalah has asked a question, "in q 2 of ex 10.4 r we allowe to use calculator to find sin Q cos then we can just tan-1( -2) and sin the value,
ReplyDeletei cant think o f another way to do it."
My response is that you don't actually need to find the value of theta, hence no calculator allowed, but you have to form equations and substitute certain identities that you already know. Let me help you with part b of question 2 as an example:
(I am using x instead of theta for convenience)
We know that tan(x)=-2 and that the signs of tan and cos have to be opposite. Then this leaves us with some angle in the fourth quadrant only where tan and cos are opp signs. Next, we know that tan(x) = sin(x)/cos(x)
Therfore, [sin(x)/cos(x)]= -2
sin(x) = -2 cos(x)
Now, you must think, what relationships between sine and cosine would be helpful?
Say we take the pythagorean relationship:
sin^2 (x) + cos^2 (x) = 1 (with this we can certainly get a relationship between the squares of sine and cosine. So, why don't we square both sides of our equation?
i.e. (sin(x))^2=(-2cos(x))^2
sin^2 (x) = 4 cos^2 (x)
Now use the pythagorean identity and substitute for cos^2 (x) so that everything is now in terms of sine. Next, the equation is easy enough to solve and you should get two values as a result of the final square rooting. One of these values will apply for sin(x) because there is a condition on this problem where tan(x) and cos(x) must have opposite signs. And so since we were restricted to the fourth quadrant we must chose the sine value from the two answers accordingly.
Hope this helps...
So, in part c of the question I have explained above, you first need to find cos(x) in a similar way and then its easy to determine sec(x) as that is just 1/cos(x). :)
ReplyDelete