If θ is an angle in standard position and its terminal side passes through the point ( -7, 24), find the exact value of sine, thetasinθ in simplest radical form.
Question
If θ is an angle in standard position and its terminal side passes through the point ( -7, 24), find the exact value of sine, thetasinθ in simplest radical form.
Solution
To find the exact value of sinθ, we first need to find the value of r, which is the distance from the origin (0,0) to the point (-7,24). We can find r using the Pythagorean theorem:
r = sqrt((-7)^2 + 24^2) r = sqrt(49 + 576) r = sqrt(625) r = 25
The sine of an angle in standard position is given by the ratio of the y-coordinate to r. So,
sinθ = y/r sinθ = 24/25
So, the exact value of sinθ in simplest radical form is 24/25.
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