Question #161491

If cos(x) = -(5/13) and π/2 ≤ x ≤ π, find the value of sin(x) and tan(x).


1
Expert's answer
2021-02-25T23:32:36-0500

Solution: Given that cos(x) = -(513\frac{5}{13}) = 513\frac{-5}{13} and π/2xπ\pi /2 \leq x \leq \pi

\therefore x is in second quadrant.

{ we know that if cos(x) = bh\frac{b}{h} then sin(x) = ah\frac{a}{h} , where aa = h2b2\sqrt{h^2 - b^2} & tan(x) = sin(x)cos(x)\frac{sin(x)}{cos(x)} }

therefore if we compare with the given cos(x) value we get:

b = -5 & h = 13

    \implies aa = 132(5)2\sqrt{13^2 - (-5)^2}

    \implies aa = 16925\sqrt{169 - 25}

    \implies aa = 144\sqrt{144}

    \implies aa = ±\pm 12

in the second quadrant value of sin(x) is always positive.

therefore, we take aa = 12


sin(x) = ah\frac{a}{h} = 1213\frac{12}{13}


tan(x) = sin(x)cos(x)\frac{sin(x)}{cos(x)} = 12/135/13\frac{12/13}{-5/13} = -125\frac{12}{5}

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