If Cot θ = -Square Root of 15/7, use the fundamental identities to find Cosθ > 0.
If cot Ø = =√15/7 then
tan Ø = -7/√15
you want tangent to be negative and cosine to be positive, ---> must be in IV
construct you triangle in quad IV
by Pythagoras, the hypotenuse is 8
and cos Ø = √15/8
To find Cosθ > 0 using the given value of Cot θ, we will make use of the fundamental identity between Cotangent (Cotθ) and Cosine (Cosθ):
Cotθ = 1/Tanθ = 1/(Sinθ/Cosθ) = Cosθ/Sinθ
Given: Cot θ = -√15/7
Using the fundamental identity, we can rewrite this equation as:
-√15/7 = Cosθ/Sinθ
Now, let's focus on finding Cosθ > 0. We know that Cosine is positive in the first and fourth quadrants. In the first quadrant, both Sinθ and Cosθ are positive. In the fourth quadrant, Sinθ is positive, but Cosθ is negative.
Since we are looking for Cosθ > 0, we should only consider the first quadrant.
From the equation -√15/7 = Cosθ/Sinθ, we can solve for Cosθ:
Cosθ = (-√15/7) * Sinθ
To find Cosθ > 0, we need to ensure that Sinθ is positive. In the first quadrant, Sinθ is positive. Therefore, we need to find the value of Sinθ.
We can use the Pythagorean identity, which states that:
Sin²θ + Cos²θ = 1
Substituting Cosθ = (-√15/7) * Sinθ in the identity, we get:
Sin²θ + [(-√15/7) * Sinθ]² = 1
Simplifying this equation, we can solve for Sinθ, and then substitute it to find the corresponding value of Cosθ.
However, without additional information or a specific value for Sinθ, we cannot determine the exact value of Cosθ > 0.