Question

evaluate [cos theta-sin theta] if [a] theta=7pi/4 [b]theta=11pi/3

Answer 1

Answer:

Step-by-step explanation:

cos11π/3-sin 11π/3    = cos( 4π -π/3)-sin(4π-π/3)=cosπ/3+sinπ/3= cos60+sin60 =1/2+√3/2=1+√3/2

Answer 2

Answer:

A) $\sqrt{2}$  B) $\frac{1+\sqrt{3} }{2}$

Step-by-step explanation:

Given

cosФ -  sin Ф

A) Ф= 7π/4

B) Ф= 11π / 4

First we have to find  Ф= 7π/4

cos 7π/4 - sin 7π/4

cos( 2π - π/4 ) - sin ( 2π - π/4 )

cos ( 2π - Ф) = cosФ

sin ( 2π - Ф) = -sin Ф

cos π/4 + sin π/4

= 1/ $\sqrt{2}$ + 1/ $\sqrt{2\\}$

= $\sqrt{2\\}$

Now we have to find  Ф= 11π / 4

cosФ -  sin Ф

cos  11π / 4 - sin 11π / 4

cos (4π - π/3 )- sin (4π - π/3 )

cos π/3 + sin π/3

= 1/2 + $\sqrt{3}$ / 2

= $\frac{1+\sqrt{3} }{2}$

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