Get the answers you need at Westonci.ca, where our expert community is always ready to help with accurate information. Experience the convenience of getting reliable answers to your questions from a vast network of knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Answer:
cosθ = [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
Given
sinθ = - [tex]\frac{5}{13}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
This is a 5- 12- 13 right triangle
with opposite = 5, adjacent = 12 , hypotenuse = 13
since θ is in 4th quadrant then cosθ > 0
cosθ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex]
The trigonometric ratio of cos θ in quadrant IV is 12/13.
What is trigonometry?
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
Sin θ = -5/13, and
θ lies in the quadrant IV.
By trigonometric ratio,
[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]
⇒ [tex]sin \theta = -\frac{5}{13}[/tex]
Here opposite side = 5 and
hypotenuse side = 13
The adjacent side can be calculated by using the Pythagoras theorem,
[tex]Hypotenuse^{2} = opposite^{2} +adjacent^{2}[/tex]
⇒ [tex]adjacent = \sqrt{hypotenuse^{2} -opposite^{2} }[/tex]
⇒ [tex]adjacent = \sqrt{13^{2} -5^{2} }[/tex]
⇒ [tex]adjacent = \sqrt{169 -25 }[/tex]
⇒ [tex]adjacent = \sqrt{144}[/tex]
⇒ [tex]adjacent = 12[/tex]
Thus [tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex]
⇒ [tex]cos \theta = \frac{12}{13}[/tex]
θ lies in the quadrant IV, so cos θ > 0.
Hence we can conclude that the trigonometric ratio of cos θ in quadrant IV is 12/13.
Learn more about trigonometry here
https://brainly.com/question/16965914
#SPJ2
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.
