Question

Given: sin = 4/5 and cos x = -5/13 ; evaluate the following expression.

cos( ∅ - x )

Answer 1

sinø=4/5

so

• cosø=3/5

And

cosx=-5/13

so

• sinx=12/13

cos(ø-x)

• sinøsinx+cosøcosx
• (4/5)(12/13)+(3/5)(-5/13)
• (48/65)-(15/65)
• 48-15/65
• 33/65

Answer 2

`\cos(\theta - x)=(33)/(65)`

Explanation:

Given:

`\sin\theta=(4)/(5)\implies \cos \theta=(3)/(5)`

`\cos x=-(5)/(13)\implies \sin x=(12)/(13)`

Using the trig identity:

`\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B`

`\begin{aligned}\implies \cos(\theta - x) &=\cos \theta \cos x + \sin \theta \sin x\\\\&=(3)/(5) \cdot -(5)/(13) + (4)/(5) \cdot (12)/(13)\\\\&=-(15)/(65) + (48)/(65)\\\\&=(33)/(65)\end{aligned}`