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b.
cos A=
c.
tan A=
3. In the figure below, if
sin x=(5)/(13), what are
cos x and tan
x ?
cos x and tan
x ?

b. $\cos A=$ $\newline$ c. $\tan A=$ $\newline$ $3$ . In the figure below, if $\sin x=\frac{5}{13}$ , what are $\cos x$ and tan $x$ ? $\cos x$ and tan $x$ ?

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Write inverse variation equations

Full solution

Q. b.

\cos A=

\newline

c.

\tan A=

\newline

3

. In the figure below, if

\sin x=\frac{5}{13}

, what are

\cos x

and tan

x

?

\cos x

and tan

x

?

Calculate $\cos x$ : Since we know $\sin x = \frac{5}{13}$ , we can use the Pythagorean identity $\sin^2 x + \cos^2 x = 1$ to find $\cos x$ . $\newline$ Let's calculate $\cos x$ : $\cos^2 x = 1 - \sin^2 x = 1 - \left(\frac{5}{13}\right)^2$ .
Find $\cos x$ : Now, we do the math: $\cos^2 x = 1 - \frac{25}{169} = \frac{169}{169} - \frac{25}{169} = \frac{144}{169}$ . So, $\cos x = \sqrt{\frac{144}{169}} = \frac{12}{13}$ or $\cos x = -\frac{12}{13}$ , but we need to know the quadrant to choose the sign.
Assume first quadrant: Since the problem doesn't specify the quadrant and we only have $\sin x$ , we'll assume $x$ is in the first quadrant where all trigonometric functions are positive. $\newline$ So, $\cos x = \frac{12}{13}$ .
Calculate $\tan x$ : Next, we find $\tan x$ using the identity $\tan x = \frac{\sin x}{\cos x}$ . Let's calculate $\tan x$ : $\tan x = \frac{\frac{5}{13}}{\frac{12}{13}}$ .
Simplify the fraction: Simplify the fraction: $\tan x = \frac{5}{13} \times \frac{13}{12} = \frac{5}{12}.$

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