find the exact value of each expression if 0 degrees< theta < 90 degrees. if tan theta= 4, find sec theta
1 + tan^2 = sec^2
sec = √(1 + tan^2)
given tanθ = 4 = 4/1 -----> y = 4, x = 1 , and θ is in quadrant I
r^2 = 4^2 + 1^2 = 17
r = √17
cosθ = 1/√17
then
sec θ = √17
To find the exact value of sec(theta), given that tan(theta) is equal to 4, we can use the relationship between secant and tangent.
The relationship is as follows:
sec^2(theta) = 1 + tan^2(theta)
Given that tan(theta) = 4, we can substitute this value into the equation:
sec^2(theta) = 1 + (4)^2
sec^2(theta) = 1 + 16
sec^2(theta) = 17
To find sec(theta), we can find the square root of both sides:
sec(theta) = sqrt(17)
Therefore, the exact value of sec(theta) is sqrt(17) when 0 degrees < theta < 90 degrees.