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.

Explanation:

We are given that cos θ = (-5/13). 

Hence, the base and the hypotenuse are in the ratio of magnitude 5/13.

Therefore, we use Pythagoras Theorem to find the length of the perpendicular. 

⇒ 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.

Therefore, we get the corresponding value of tan θ = sin θ/cos θ = 12/5 which is greater than 0.

Hence, if cos θ = (-5/13), tanθ > 0, then the value of sin θ = -12/13.