Question

Trigonometry A level question.?

Answer 1

(i)

The given expression is 3cos x + 4sin x.

To Express this in terms of .

First we simplify .

Now consider  and then a² + b²

Therefore

To find the value of α,

Now to express a cosx + b sin x in terms of then and .

The Equation is 3cos x + 4sin x where a=3 and b=4.

Therefore the equation 3cos x + 4sin x is expressed as .

Answer 2

(ii)

The given equation is 3cosx + 4sinx = 4.5.

First we write 3cosx + 4sinx = 5 cos(x - 53.13)   (From (i) )

Rewrite the equation as 5 cos(x - 53.13) = 4.5

cos(x - 53.13) = 0.9

x - 53.13 = 2nπ ±25.84

for n=0

x - 53.13 = 25.84

x = 79°

Therefore x = 79°.