If cos θ = (-5/13), tan θ > 0, what is sin θ?
Trigonometry deals with the relationships between sides and angles of triangles. They have many applications in calculus, linear algebra as well as geometry. Let's solve a problem related to the concepts of trigonometry.
Answer: If cos θ = (-5/13), tanθ > 0, then the value of sin θ = -12/13.
Let's understand the solution in detail.
We are given that cos θ = (-5/13).
Hence, the base and the hypotenuse are in the ratio of magnitude 5/13.
⇒ perpendicular = √(132 - 52) = 12 units.
Now, we see that cos θ is negative, hence, θ can't be in the first or the fourth quadrant.
Also, it is given that tan θ > 0, so θ can't be in the second quadrant.
Therefore, θ must definitely be in the third quadrant.
Since sin θ < 0 in the third quadrant:
⇒ sin θ = perpendicular / hypotenuse = -12/13.
Hence, if cos θ = (-5/13), tanθ > 0, then the value of sin θ = -12/13.