Question

The statement tan θ =12/5, csc θ = -13/5, and the terminal point determined by θ is in quadrant 3

a. cannot be true because if tan θ =-12/5, then csc θ = -13/12
b. cannot be true because 12 elevated by 2 5 elevated by 2 different than 1

Answer 1

The statement tan θ =12/5, csc θ = -13/5, and the terminal point determined by θ is in quadrant 3 a. cannot be true because if tan θ =-12/5, then csc θ = -13/12 b. cannot be true because 12 elevated by 2 5 elevated by 2 different than 1

Step-by-step explanation:

The statement tan θ =12/5, csc θ = -13/5, and the terminal point determined by θ is in quadrant 3 a. cannot be true because if tan θ =-12/5, then csc θ = -13/12 b. cannot be true because 12 elevated by 2 5 elevated by 2 different than 1

To solve this problem, we need to use the definitions of tangent (tan) and cosecant (csc), as well as the fact that the terminal point determined by θ is in quadrant 3. In quadrant 3, both the x and y coordinates are negative.

Given that tan θ =12/5, we can find the value of θ by taking the inverse tangent (tan⁻¹) of 12/5. Similarly, we can find the value of csc θ by taking the reciprocal of sin θ, which is equal to 1/sin θ. Since sin θ = y/r, where y is the opposite side and r is the hypotenuse, we can use the Pythagorean theorem to find the value of r. Once we have the values of θ and r, we can find the values of x and y using the definitions of sine (sin) and cosine (cos).