Question

Evaluate (cos θ - sin θ) if (a) θ = $\frac{7\pi}{4}$(b) θ = $\frac{11\pi}{3}$

Answer 1

Please see the attachment

Answer 2

Answer:

√2

(1 + √3)/2

Step-by-step explanation:

cos θ - sin θ

θ = 7π/4

= Cos (7π/4) - Sin (7π/4)

= Cos(2π - π/4) - Sin(2π - π/4)

= Cos(π/4) - (-Sin(π/4))

= Cos(π/4) + Sin(π/4)

= 1/√2  + 1/√2

= 2/√2

= √2

cos θ - sin θ

θ = 11π/3

= Cos (11π/3) - Sin (11π/3)

= Cos(4π - π/3) - Sin(4π - π/3)

= Cos(π/3) - (-Sin(π/3))

= Cos(π/3) + Sin(π/3)

= 1/2  + √3/2

= (1 + √3)/2