Special angle question!!! (1 Viewer)

[samsonhohoho]

given that: sinθ = 3/4 and 90 degree < θ < 180 degree

find as a single expression with rational denominator, the exact value of
i) cos θ
ii) cos θ + tan θ

b) find all values of θ so that sin 2θ = 1/4 and 0 degree < θ < 360 degree

Show all working please. Thanks

 

[nightweaver066]

Since , we can construct this.

Now find the unknown side using pythagoras, and now you can do i) and ii) (using & )

For b), do you mean or ? It'd be a bit messy with

 

[samsonhohoho]

sin 2 θ

 

[nightweaver066]

We want solutions . This is the same as (everything multiplied by 2)

So then we need to consider the solutions for 2 revolutions for



Divide both sides by 2 to get the answer. Sorry that i can't simplify it, i don't have a calculator available atm lol

 

[Peeik]

Just briefly looked at part (b) and you solve it like a normal trig equation.

Sin2θ=1/4 for 0<θ<360.

Change the domain to suit the equation i.e. 0<2θ<720. Now solve the equation within this domain.

sin2θ=1/4 for 0<2θ<720

2θ=14 , 166 , 374, 526 (to the nearest degree)
θ = 7, 83, 187, 236.