Question

24. If 3tane = 4, find the value of sine and sece​

Answer 1

Step-by-step explanation:

Given = $3 \tan \theta = 4$

$\tan \theta = \frac{3}{4}$

$\tan \theta = \frac{opposite}{adjacent} = \frac{3}{4}$

By using Pythagoras theorem,

${H }^{2} = { P}^{2} + { B }^{2}$

${H }^{2} = {3}^{2} + {4}^{2}$

${H}^{2} = 9 + 16$

$H = \sqrt{25}$

$H = 5$

$\sec \theta = \frac{hypotenuse}{adjacent} = \frac{5}{4}$

$\sin \theta = \frac{opposite}{hypotenuse} = \frac{3}{5}$

Answer 2

Answer:

$\sin \: e = \frac{4}{5} \: and \: \sec \: e = \frac{5}{3}$

Step-by-step explanation:

$let \: perpendicular \: = p \\ base = b \\ and \: hypotenuse \: = h \\ 3 \tan \: e = 4 \\ = > \tan \: e = \frac{4}{3} = \frac{p}{b} \\ let \: p = 4x \\ b = 3x \\ {h}^{2} = {p}^{2} + {b}^{2} \\ = > h = \sqrt{ {p}^{2} + {b}^{2} } \\ = > h = \sqrt{ {4x}^{2} + {3x}^{2} } \\ = > h = \sqrt{16 {x}^{2} + 9 {x}^{2} } \\ = > h = \sqrt{ {25x}^{2} } \\ = > h = 5x \\ \sin \: e = \frac{p}{h} = \frac{4x}{5x} = \frac{4}{5} \\ \sec \: e = \frac{h}{b} = \frac{5x}{3x} = \frac{5}{3}$