Harmonic form & trig modelling

Given that

 $2\sin\ x-\sqrt{5}\cos\ x\equiv-3\cos\ \left(x+a\right)$  .
Find the value of  $a$  in degrees.

• 48.1

• 41.8

• 33.7

• 36.7

 $\cos\left(x\right)\ -\sqrt{3}\sin\left(x\right)\equiv R\cos\left(x+a\right)$  .
Given that  $R>0$ , find  $R$   . 

•  $\sqrt{10}$  

•  $\sqrt{2}$  

•  $\sqrt{3}$  

•  $2$  

Part 1:
 $f\left(x\right)=\sin\left(x\right)+3\cos\left(x\right).$  

By writing  $f\left(x\right)=R\sin\left(x+a\right)$  , find the maximum value of  $f\left(x\right)$  .

• 10

• 4

•  $\sqrt{10}$  

• 3

Part 2:
 $f\left(x\right)=\sin\left(x\right)+3\cos\left(x\right)$  

Using your workings from the last question, find the only value of  $0\le a\le90\degree$  where this maximum value occurs.

• 69.2

• 0

• 71.6

• 18.4

• 0.1m

• 0.1cm

• 0.7m

• 1.4m

• 80

• 105

• 130

• 70

(t is in radians)

• March

• April

• May

• June