Given tan A =4/3. find the trigonometric ratios of the angle A. ​

2 thoughts on “Given tan A =4/3. find the trigonometric ratios of the angle A. ​”

1. Answer:

   [tex] \tan(a) = \frac{p}{b} \\ p = 4 \:, \: b \: = 3 \\ {h}^{2} = {p}^{2} + {b}^{2} \\ {h}^{2} = {4}^{2} + {3}^{2} \\h = \sqrt{25} \\ h = 5 \\ \sin(a) = \frac{p}{h} = \frac{4}{5} \\ \csc(a) = \frac{5}{4} \\ \cos(a) = \frac{b}{h} = \frac{3}{5} \\ \sec(a) = \frac{5}{3} \\ \cot(a) = \frac{3}{4} [/tex]

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2. Topic:-

   Trigonometry

   Question:-

   [tex]Given\: tan\theta=4/3. find\:the\:trigonometric\: ratios\: of \:the\: angle\: \theta [/tex]

   Solution:-

   [tex]Given tan \theta=4/3 [/tex]

   [tex] We\: know\: that \:tan\theta =\dfrac{Opposite\:side}{Adjacent\:side} [/tex]

   [tex] Here, \:Opposite\:side= 4 \: and Adjacent\:side=3 [/tex]

   [tex] We \:need \:Hypotenuse\:side \: here [/tex]

   [tex] We\: know\: that\:Pythageorous\:theorem[/tex]

   [tex] Hypotenuse²=Opposite\:side²+Adjacent\:side²[/tex]

   [tex] Hypotenuse²= 4²+3² [/tex]

   [tex] Hypotenuse²= 16+9 [/tex]

   [tex] Hypotenuse²= 25 [/tex]

   [tex] Hypotenuse=\sqrt{25} [/tex]

   [tex] Hypotenuse= 5[/tex]

   [tex] Now\:we\:got\:all\:sides [/tex]

   [tex] Sin\theta =\dfrac{Opposite\:side}{Hypotenuse\:side}[/tex]

   So, [tex] Sin\theta=\dfrac{4}{5} [/tex]

   [tex] cos\theta=\dfrac{Adjacent\:side}{Hypotenuse\:side}[/tex]

   [tex] cos\theta=\dfrac{ 3}{5} [/tex]

   [tex] cot\theta=\dfrac{Adjacent\:side}{Opposite\:side} [/tex]

   [tex] cot\theta=\dfrac{3}{4}[/tex]

   [tex] csc\theta=\dfrac{Hypotenuse\:side}{Opposite\:side}[/tex]

   [tex] csc\theta=\dfrac{5}{4} [/tex]

   [tex] sec\theta= \dfrac{Hypotenuse}{Adjacent} [/tex]

   [tex] sec\theta= \dfrac{ 5}{3} [/tex]

   More Information:-

   Trigon metric Identities

   sin²θ + cos²θ = 1

   sec²θ – tan²θ = 1

   csc²θ – cot²θ = 1

   Trigometric relations

   sinθ = 1/cscθ

   cosθ = 1 /secθ

   tanθ = 1/cotθ

   tanθ = sinθ/cosθ

   cotθ = cosθ/sinθ

   Trigonmetric ratios

   sinθ = opp/hyp

   cosθ = adj/hyp

   tanθ = opp/adj

   cotθ = adj/opp

   cscθ = hyp/opp

   secθ = hyp/adj

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