Question

If tan ø = 12/5 and cos ø = -5/13 then what is sin ø?

A. 12
B. 5/13
C. -5/13
D. 12/13
E. -12/13

Answer 1

E

Explanation:

using the trigonometric identity

sin²x + cos²x = 1, then

sinx = ±
`√(1-cos^2x)`

Since tanΦ > 0 and cosΦ < 0 then Φ is in the third quadrant

where sinΦ < 0

sinΦ = -
`√(1-(-5/13)^2)` = -
`\sqrt{1-(25)/(169) }` = -
`\sqrt{(144)/(169) }` = -
`(12)/(13)` → E