Answered

Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Join our Q&A platform to get precise answers from experts in diverse fields and enhance your understanding. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

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

cos( ∅ - x )

Sagot :

semsee45

Answer:

[tex]\cos(\theta - x)=\dfrac{33}{65}[/tex]

Step-by-step explanation:

Given:

[tex]\sin\theta=\dfrac{4}{5}\implies \cos \theta=\dfrac{3}{5}[/tex]

[tex]\cos x=-\dfrac{5}{13}\implies \sin x=\dfrac{12}{13}[/tex]

Using the trig identity:

[tex]\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B[/tex]

[tex]\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}[/tex]

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
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.