Answer to Question #161491 in Trigonometry for Ella

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) = -("\\frac{5}{13}") = "\\frac{-5}{13}" and "\\pi \/2 \\leq x \\leq \\pi"

"\\therefore" x is in second quadrant.

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

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

b = -5 & h = 13

"\\implies" "a" = "\\sqrt{13^2 - (-5)^2}"

"\\implies" "a" = "\\sqrt{169 - 25}"

"\\implies" "a" = "\\sqrt{144}"

"\\implies" "a" = "\\pm" 12

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

therefore, we take "a" = 12


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


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

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