sin theta= 7/25, 0< theta < pi/2 cos beta=8/17, 0, beta, pi/2 Find(theta+ beta)
To find the value of (θ + β) given the values of sin θ and cos β, we need to use the trigonometric identities.
First, let's find the values of sin θ and cos β using the given information.
Given:
sin θ = 7/25
cos β = 8/17
We can use the Pythagorean identity sin^2 θ + cos^2 θ = 1 to find cos θ.
sin^2 θ = (7/25)^2
cos^2 θ = 1 - sin^2 θ
cos^2 θ = 1 - (49/625)
cos^2 θ = 576/625
Taking the square root of both sides, we get:
cos θ = ±√(576/625)
Since 0 < θ < π/2, we can conclude that cos θ = √(576/625) = 24/25
Now, let's use the sum formula for cosine to find cos(θ + β):
cos(θ + β) = cos θ cos β - sin θ sin β
cos(θ + β) = (24/25)(8/17) - (7/25)(√(1 - (8/17)^2))
cos(θ + β) = (24/25)(8/17) - (7/25)(√(1 - 64/289))
cos(θ + β) = (24/25)(8/17) - (7/25)(√(225/289))
cos(θ + β) = (24/25)(8/17) - (7/25)(15/17)
cos(θ + β) = 192/425 - 105/425
cos(θ + β) = 87/425
Now, to find the value of (θ + β), we can use the inverse cosine function (arccos):
θ + β = arccos(87/425)
Therefore, the value of (θ + β) is arccos(87/425).