Question

Draw a right triangle with one leg value is 4 and the other leg value is 3. Use the triangle to find the exact values of the six trigonometric functions of

Answer 1

Step-by-step explanation:

Draw a right triangle with one leg value is 4 and the other leg value is 3

The triangle is attached below

To find hypotenuse , use Pythagorean theorem

$c^{2} =a^{2} +b^{2} \\c^{2} =3^{2} +4^{2} \\\\c^{2} =25 \\\\c=\sqrt{25} =5$

opposite side = 4, adjacent side =3 and hypotenuse = 5

Apply trigonometric ratios

$sin(A)=\frac{opposite}{hypotenuse}=\frac{4}{5}$

$cos(A)=\frac{adjacent}{hypotenuse}=\frac{3}{5}$

$tan(A)=\frac{opposite}{adjacent}=\frac{4}{3}$

$cosec(A)=\frac{hypotenuse}{opposite}=\frac{5}{4}$

$sec(A)=\frac{hypotenuse}{adjacent}=\frac{5}{3}$

$cot(A)=\frac{adjacent}{opposite}=\frac{3}{4}$