If [tex]\tan x = \frac{3}{4}[/tex] and [tex]0^\circ \leq x \leq 90^\circ[/tex], then what is [tex]\cos x[/tex]?

Please explain the work behind the solution.

Tanx = 3/4 = Y/X = opps/adj
sqrt(3^2+4^2) = 5 = hypotenuse
Cos is adj/hyp
Cosx = 4/5

Answered by wblanco4600 | 2024-06-10

t an x = 4 3 ​ t an x = cos x s in x ​ cos x s in x ​ = 4 3 ​ → s in x = 4 3 ​ cos x ( ∗ ) s i n 2 x + co s 2 x = 1 s u b s t i t u t e ( ∗ ) ( 4 3 ​ cos x ) 2 + co s 2 x = 1 16 9 ​ co s 2 x + co s 2 x = 1
16 15 ​ co s 2 x = 1 / ⋅ 25 16 ​ co s 2 x = 25 16 ​ cos x = 25 16 ​ ​ cos x = 5 4 ​

Answered by Anonymous | 2024-06-24

Given tan x = 4 3 ​ , we determined cos x = 5 4 ​ using the relationship between tangent, sine, and cosine alongside the Pythagorean identity. This solution is valid within the range specified for x .
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Answered by Anonymous | 2024-10-12