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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
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