C3 Trig questions!!!

Could somebody please help me with this:

7) The angles x and y are acute angles such that sinx= 2 / √5 and cosy= 3 / √10.
a) Show that cos2x=-3/5. (I got -4?!)
b) Find the value of cos2y (Again, i got the wrong answer...).
c) Show without using your calculator, that:
i) tan (x+y) = 7
ii) x-y = π/4.

8) Given that sinxcosy=1/2 and cosxsiny=1/3,
a) show that sin(x+y)=5sin(x-y)
given also that tany=k, express in terms of k,
b) tan x
c) tan 2x

Reply 1

Malik

12

turtle2

Could somebody please help me with this:

7) The angles x and y are acute angles such that sinx= 2 / √5 and cosy= 3 / √10.
a) Show that cos2x=-3/5. (I got -4?!)
b) Find the value of cos2y (Again, i got the wrong answer...).
c) Show without using your calculator, that:
i) tan (x+y) = 7
ii) x-y = π/4.

8) Given that sinxcosy=1/2 and cosxsiny=1/3,
a) show that sin(x+y)=5sin(x-y)
given also that tany=k, express in terms of k,
b) tan x
c) tan 2x

a) cos2x≡1−2sin²x
= 1-2(2/√5)²
=1-8/5 = -3/5

b)cos2y≡2cos²y−1
=2(3/√10)²-1
=18/10 - 1
=4/5

c) Draw a triangle and put the values of sin and cos on it. And you will see that=> tanx=2 tany=1/3

i)tan(x+y)=(tanx+tany)/(1-tanxtany)
=(7/3)/(1-(2/3))
=7

ii)tan(x-y)=(tanx-tany)/(1+tanxtany)
=(5/3)/(5/3)
=1
.:.x-y=45°
=π/4

Reply 2

turtle2

OP

7

Ohh i see. Thanks!

Could somebody also pls help me with these:
9b)sin3θcos2θ=sin2θcos3θ 0«θ«π
c)sin(θ+40)+sin(θ+50)=0 0«θ«360
e)2sinθ=1+3cosθ 0«θ«360
f)cos5θ=cos3θ 0«θ«π
g)cos2θ=5sinθ -π«θ«π (these last ones are quite similar...i think i need to use Rcos/sin(θ+a), but im not sure...and how do i know which one? What do I do?!?!)

Please help!

Reply 3

Malik

12

turtle2

Ohh i see. Thanks!

Could somebody also pls help me with these:
9b)sin3θcos2θ=sin2θcos3θ 0«θ«π
c)sin(θ+40)+sin(θ+50)=0 0«θ«360
e)2sinθ=1+3cosθ 0«θ«360
f)cos5θ=cos3θ 0«θ«π
g)cos2θ=5sinθ -π«θ«π (these last ones are quite similar...i think i need to use Rcos/sin(θ+a), but im not sure...and how do i know which one? What do I do?!?!)

Please help!

Less ones pretty straight foward
g)cos2x=1-2sin²x
cos2θ=5sinθ
1-2sin²θ=5sinθ
2sin²θ+5sinθ-1=0
you should be able to solve that quadratic and get θ.

C3 Trig questions!!!

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