If tan x 5/8 find sin (90-x) answer in 3 s.f.g
Since tan x = opposite/adjacent, we can assume a right triangle where the opposite side is 5 and the adjacent side is 8. Using the Pythagorean Theorem, we can find that the hypotenuse is √(5^2 + 8^2) = √89.
Now, sin (90-x) = cos x (since sin (90-x) is the opposite of the adjacent side in the right triangle for angle x).
cos x = adjacent/hypotenuse = 8/√89 ≈ 0.846 (rounded to 3 significant figures).
Therefore, sin (90-x) ≈ 0.846.
To find the value of sin(90 - x), we can use the identity sin(90 - x) = cos(x).
Given that tan(x) = 5/8, we can solve for cos(x) using the Pythagorean identity: tan^2(x) + 1 = sec^2(x).
Substituting the given value: (5/8)^2 + 1 = sec^2(x)
25/64 + 1 = sec^2(x)
89/64 = sec^2(x)
Taking the square root of both sides, we get: √(89/64) = |sec(x)|
√(89/64) = sec(x)
Since sec(x) represents the reciprocal of cos(x), we have: cos(x) = 8/√(89) = 8√(89)/89
Now, we can find sin(90 - x) by substituting the value of cos(x) into the identity. sin(90 - x) = cos(x)
sin(90 - x) = 8√(89)/89
Rounding to three significant figures, the value of sin(90 - x) is approximately 0.090