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

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=√(25) =5`

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

Apply trigonometric ratios

`sin(A)=(opposite)/(hypotenuse)=(4)/(5)`

`cos(A)=(adjacent)/(hypotenuse)=(3)/(5)`

`tan(A)=(opposite)/(adjacent)=(4)/(3)`

`cosec(A)=(hypotenuse)/(opposite)=(5)/(4)`

`sec(A)=(hypotenuse)/(adjacent)=(5)/(3)`

`cot(A)=(adjacent)/(opposite)=(3)/(4)`