Respuesta :
Answer:
-7/25.
Step-by-step explanation:
From the given point P we see that the hypotenuse = √(3*2 + 4^2) = 5.
So cos θ = 3/5
cos 2 θ = 2 cos^2 θ - 1
= 2 * (3/5)^2 -1
= -7/25.
The value of cos 2θ is -7/25.
The correct answer is option B.
How do you evaluate the given angle of cosine?
Given that the position of angle [tex]\theta[/tex] in the first-quadrant is P (u, v) = (3, 4).
Hence the hypotenuse h from the given point P will be calculated as below.
[tex]h = \sqrt{b^2 + l^2}[/tex]
Where h is the hypotenuse, b is the base and l is the side of the right-angle triangle.
[tex]h = \sqrt{3^2 + 4^2}[/tex]
[tex]h = \sqrt{9+16} = \sqrt{25}[/tex]
[tex]h = 5[/tex]
Now the angle of cosine from the given point P will be,
[tex]cos \theta = \dfrac {3}{5}[/tex]
Thus,
[tex]cos\; 2\theta = 2\;cos^2\;\theta - 1[/tex]
Substituting the value of angle of cosine, we get,
[tex]cos\;2\theta = 2\times {\dfrac {3}{5}}^2 -1[/tex]
[tex]cos\;2\theta = 2\times \dfrac {9}{25} -1[/tex]
[tex]cos \;2\theta = -\dfrac {7}{25}[/tex]
Thus, the correct answer is option B. The value of cos 2θ is -7/25.
To know more about the angle of cosine, follow the link given below.
https://brainly.com/question/4637040.
