Given cosθ=3/7 and 0≤θ≤π/2 find sinθ and tanθ
sin^2 T = 1 - cos^2 T
sin^2 T = 1 - 9/49
sin^2 T = 40/49
sin T = (2/7) sqrt 10
and tan T = sin T/cos T
or, just draw the triangle and label the sides. The missing side is √(49-9) = √40
Then you can read off all the trig functions just by looking at the sides and using the proper ones.
To find sinθ and tanθ given cosθ=3/7 and 0≤θ≤π/2, we can use the Pythagorean identity.
The Pythagorean identity is sin^2θ + cos^2θ = 1.
We are given that cosθ = 3/7. Using this information, we can substitute cosθ in the Pythagorean identity to solve for sinθ.
sin^2θ + (3/7)^2 = 1
sin^2θ + 9/49 = 1
sin^2θ = 1 - 9/49
sin^2θ = 40/49
Now, to find sinθ, we take the square root of both sides of the equation.
sinθ = √(40/49)
sinθ = √40 / √49
sinθ = 2√10 / 7
To find tanθ, we can use the relationship between sinθ and cosθ. The tangent of an angle is defined as the ratio of the sine of the angle to the cosine of the angle.
tanθ = sinθ / cosθ
tanθ = (2√10 / 7) / (3/7)
tanθ = 2√10 / 3
So, sinθ = 2√10 / 7 and tanθ = 2√10 / 3.