1994 Past paper question (1 Viewer)

[BenBrownTown]

Question 5
Find All angles θ, where 0 ≤ θ < 2π, for which

√3 sin θ - cos θ = 1
could anyone please post working how to find solution with explanation please and thankyou

 

[deswa1]

I don't have time for a full worked solution sorry but I'll give the general method and then hopefully you can do it or someone can post a full solution.

Basically you are using whats known as the auxilliary angles method. You basically change the LHS into the form of Asin(theta-b) for some A,b (your textbook should show you how to do this) and then you solve like an ordinary trig equation.

OR, you can use the t-formula if you are more algebraically inclined and then solve for t etc.

 

[shongaponga]

I'll type up a solution now, give me a minute

 

[BenBrownTown]

I don't have time for a full worked solution sorry but I'll give the general method and then hopefully you can do it or someone can post a full solution.

Basically you are using whats known as the auxilliary angles method. You basically change the LHS into the form of Asin(theta-b) for some A,b (your textbook should show you how to do this) and then you solve like an ordinary trig equation.

OR, you can use the t-formula if you are more algebraically inclined and then solve for t etc.

I'll type up a solution now, give me a minute

all good i understand now i just didnt see that you needed to use auxilliary methods, thankyou very much makes sense now

 

[BenBrownTown]

Basically you are using whats known as the auxilliary angles method. OR, you can use the t-formula if you are more algebraically inclined and then solve for t etc.

sorry for the double post but correct me if im wrong but i can sketch them both on the same axis and take values from the sketch

 

[deswa1]

sorry for the double post but correct me if im wrong but i can sketch them both on the same axis and take values from the sketch

How on earth are you going to sketch that accurately? Your answer will most likely be an irrational number -> there's no way you'd get the answer from a graph

For these questions, stick to algebraic or trig methods

 

[BenBrownTown]

very true, It is simple to get a decimal value but otherwise it is extremely difficult.

 

[Focus is Key]

Would using the T-Methods work as well?

 

[deswa1]

Would using the T-Methods work as well?

Yep