G4

Question 1

How to draw sin x cos x and tan x

Answer 1

sin x starts from 0,0 and goes up to peak at 90,1. It goes down to 180,0. It goes lower to 270,-1. It rises up to 360,0

cos x starts at 0,1. It goes down to 90,0. It goes lower to 180,-1. it rises to 270,0. it goes back up to 360,1.

tan x has an asymptote at 90 and 270 degrees. It goes from 0 to 90 in sort of na exponential and doesn’t touch at asymptote. It starts just a little after 90 (doesn’t touch asymptote) at -1 and goes to 180,0. It then does the same and repeats

Question 2

If the eq of a circle is x^2 + y^2 = 100 what’s the radius

Answer 2

the last number rooted (10 as root of 100 is 10)

Question 3

What is the sine rule and how do you find out a missing angle/side with it

Answer 3

A/sin(a) = B/sin(b) = C/sin(c)

Given/sin(given) = GivenB/sin(x)
Givensin(x) = GivenBsin(given)
sin(x) = GivenB*sin(given)/Given
x = sin^-1 answer of above

Given/sin(given) = X/sin(givenB)
X = Given*sin(givenB)/sin(given)

we use this for non right angle triangles

Question 4

what is cosine rule for finding a side and an angle and in what scenario do we use both

Answer 4

side: a^2 = b^2 + c^2 - 2bc cos(A)
(when we have 2 sides and an angle linking those 2 sides and we want to find the opposite side to that angle)

angle: cos(A) = b^2 + c^2 - a^2 // 2bc
A = cos^-1(ans)
(when we have all the sides and we need to find one angle)

we use this for non right angle triangles

Question 5

area of triangle for any triangles

Answer 5

1/2 ab sin(c)

Question 6

How do we find the area of the segment

Answer 6

we need to find the area of the whole triangle (angle/360 * pi r^2)

We need to find area of the triangle (if we remove the curved bit (sector) we get a triangle) by doing 1/2 ab sin(c)

subtract the whole by the triangle

Question 7

3 Qualities about bearings you MUST know

Answer 7

They are an angle starting from NORTH
going in a CLOCKWISE motion
and they use 3 FIGURES (ie: 080)

Question 8

If a question asks to do a bearing from point A, and an arrow is facing upwards to show north how would you use a compass to draw it

Answer 8

You would turn your protractor 90 degrees right but still keep the middle/centre on point A. This ensures that the bearing is directly measured from north as the 0 degrees on the protractor is lined up with the north line

Question 9

(MAY NOT BE PART OF THE TOPIC): for inequalities on a graph, if x^2 > -3x - 18 then what do you do to find the solution

Answer 9

Rearrange to ax^2 +bx + c = 0
Factorise to get 2 solutions
Since the inequality would be greater than 0 then if you imagine a graph, yhe solutions mist be anywhere where the y would be above 0