Answer :
Question:
if tan[tex]\theta[/tex] = 12/5 and cos[tex]\theta[/tex] = -5/13, then what is sin[tex]\theta[/tex]
Answer:
[tex]sin \theta = \frac{ -12}{13}[/tex]
Step-by-step explanation:
Given:
tan[tex]\theta[/tex] = 12/5
cos[tex]\theta[/tex] = -5/13
To find:
sin[tex]\theta[/tex] = ?
Solution:
We can find the sin[tex]\theta[/tex] value by using the tan ratio and cosine ratio
[tex]cos = \frac{ adjacent }{hypotenuse} = \frac{ -5}{13}[/tex]
[tex]sin = \frac{ opposite}{hypotenuse}[/tex]
[tex]sin \theta = tan \theta \times cos\theta[/tex]
[tex]sin \theta = \frac{opposite}{adjacent} \times \frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{ opposite}{hypotenuse}[/tex]
On substituting the values,
[tex]sin \theta = \frac{ 12}{5} \times \frac{-5}{13}[/tex]
[tex]sin \theta = \frac{ -12}{13}[/tex]