Question

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

Answer 1

Answer:

$\cos(\theta - x)=\dfrac{33}{65}$

Step-by-step explanation:

Given:

$\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}$

$\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}$

Using the trig identity:

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

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

Answer 2

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