Some Quick Qs (1 Viewer)

[Mudkip94]

1. The interval joining the points A(-1,7) and B(5,2) is divided by a point P(x,y) in the ratio k:1. The point P lies on the line 5x-4y=1. Find the value of k.

2. Given sinθ=0.4 and θ is acute, write down the exact values of:
b) cos(270-θ)
d) cot(360-θ)

3. Solve for -180°≤θ≤180°
i) cosθ=0.187
iii) 4sinθ+3=0

Thanks!

 

[pqd123]

1.
P = [(-1 + 5k)/(k +1) , (7 + 2k)/(k+1)]
since it lies on 5x-4y=1
[5(-1+5k)/(k+1)] - [4(7+2k)/(k+1)] = 1
(17k-33)/(k+1) = 1
16k - 32 = 0
k = 2

2.
draw the triangle
hyp = 5
opp = 2
adj = √21
cos(270 - θ) = -cos(90 - θ) = -sinθ = -0.4
cot(360 - θ) = -cotθ = √21/2

 

[pqd123]

3.a.
0.187 is positive so θ is in the first and 4th quadrant
θ = 79.22, -79.22

b.
sinθ = -3/4
-3/4 is negative so θ is in the 3rd and 4th quadrant
θ = -48.59, -131.41

 

[Mudkip94]

A bit late because the stuff was due today but thanks anyway!