Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The terminal side of 0 is in quadrant IV and sin 0= -5/13 What is cos 0?

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

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.