Question

If X and Y are complementary angles, sinX =15/17 and cos X = 8/17, find each of the following :

a. tanX=

b. sinY=

c. cosY=

d. tsnY=

Answer 1

$tan X = \frac{Sin X}{Cos X}$

$tan X = \frac{\frac{15}{17}}{\frac{8}{17}}$

$tan X = \frac{15}{17} × \frac{17}{8}$

$tan X = \frac{15}{8}$

Since X and Y are complementary angles

$Sin Y = Cos X = \frac{8}{17}$

$=>Sin Y = \frac{8}{17}$

$Cos Y = Sin X = \frac{15}{17}$

$=> Cos Y= \frac{15}{17}$

$tan Y = \frac{Sin Y}{Cos Y}$

$tan Y = \frac{\frac{8}{17}}{\frac{15}{17}}$

$=> tan Y = \frac{8}{17} × \frac{17}{15}$

$tan Y = \frac{8}{15}$