Final answer:
To find the value of 2θ, use the given information of sin θ and cos θ. Use the trigonometric identity sin^2 θ + cos^2 θ = 1 to solve for cos θ. Then use the double-angle formula for cosine to find the value of 2θ.
Step-by-step explanation:
To find the value of 2θ, we need to use the given information of sin θ and cos θ. We know that sin θ = -√3/5 and cos θ > 0. We can use the trigonometric identity sin^2 θ + cos^2 θ = 1 to find cos θ. Since sin θ = -√3/5, we can substitute this value into the equation and solve for cos θ.
sin^2 θ + cos^2 θ = 1
((-√3/5)^2) + cos^2 θ = 1
3/5 + cos^2 θ = 1
cos^2 θ = 1 - 3/5
cos^2 θ = 2/5
cos θ = √(2/5)
Since cos θ > 0, cos θ = √(2/5)
We can now find the value of 2θ by using the double-angle formula for cosine: cos(2θ) = 2cos^2 θ - 1
cos(2θ) = 2(√(2/5))^2 - 1
cos(2θ) = 2(2/5) - 1
cos(2θ) = 4/5 - 1
cos(2θ) = -1/5
Since cos(2θ) = -1/5, we can find the value of 2θ by taking the inverse cosine of -1/5: 2θ = cos^(-1)(-1/5)
The decimal value of 2θ is approximately -78.46°.