Question

Let (-2,5) be a point on the terminal side of θ. Find sin θ, sec θ, tan θ.

a) sin θ = -2/5, sec θ = -5/2, tan θ = 2/5
b) sin θ = 2/5, sec θ = -5/2, tan θ = -2/5
c) sin θ = -2/5, sec θ = -2/5, tan θ = 2/5
d) sin θ = 2/5, sec θ = -2/5, tan θ = -2/5

Answer 1

The values for sin θ, sec θ, and tan θ given the point (-2,5) are calculated using the right triangle properties, with sin θ = 5/√29, sec θ = √29/2, and tan θ = -5/2. The options provided do not include the correct answer after simplifying the expressions.

Step-by-step explanation:

To find the values of sin θ, sec θ, and tan θ given the point (-2,5) on the terminal side of angle θ, we first recognize that the point's coordinates represent the lengths of the sides of a right triangle formed with the x-axis. In this context, -2 is the length of the side adjacent to θ (x-coordinate), 5 is the length of the side opposite θ (y-coordinate), and the hypotenuse is the distance from the origin to the point, which can be calculated using the Pythagorean theorem.

The hypotenuse is √((-2)² + 5²) = √(4+25) = √29. Using these values we calculate:

• sin θ = opposite/hypotenuse = 5/√29
• sec θ = 1/cos θ = 1/(adjacent/hypotenuse) = -√29/(-2)
• tan θ = opposite/adjacent = 5/(-2)

Therefore, the correct answer is not presented in the options provided and we would need to simplify further to find the values

sin θ = 5/√29, sec θ = √29/2, tan θ = -5/2.