Question

Given that tan x =3/7find cos (90-x) giving you answer in 4 significant figures​

Answer 1

Answer:

$\cos \left(90 ^\circ - x\right) \approx 0.1688$

Step-by-step explanation:

We are given that:

$\displaystyle \tan x = \frac{3}{7}$

And we want to find the value of:

$\displaystyle \cos \left(90^\circ - x\right)$

Recall that by definition, tan(θ) = sin(θ) / cos(θ). Hence:

$\displaystyle \frac{\sin x }{\cos x} = \frac{3}{7}$

And by definition, sin(θ) = cos(90° - θ). Hence:

$\displaystyle \frac{\cos \left(90^\circ - x\right)}{\cos x} = \frac{3}{7}$

Multiply:

$\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \cos x$

Find cosine. Recall that tangent is the ratio of the opposite side to the adjacent side. Therefore, the opposite side is 3 and the adjacent side is 7.

Thus, by the Pythagorean Theorem, the hypotenuse will be:

$\displaystyle h = \sqrt{3^2 + 7^2} = \sqrt{58}$

Cosine is the ratio of the adjacent side to the hypotenuse. Therefore:

$\displaystyle \cos x = \frac{7}{\sqrt{58}}$

Thus:

$\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \left(\frac{3}{\sqrt{58}}\right)$

Use a calculator. Hence:

$\cos \left(90 ^\circ - x\right) \approx 0.1688$