Question

Question 28 Let be an angle in quadrant such that. Find the exact values of and.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Since Θ is an angle in the third quadrant, then secΘ < 0 and tanΘ > 0

Using the identity

sec x = $\frac{1}{cosx}$ , then

cos x = - $\sqrt{1-sin^2x}$

         = - $\sqrt{1-(-3/5)^2}$ = - $\sqrt{1-\frac{9}{25} }$ = - $\sqrt{\frac{16}{25} }$ = - $\frac{4}{5}$, thus

secΘ = $\frac{1}{-\frac{4}{5} }$ = - $\frac{5}{4}$

---------------------------

Using the identity

tan x = $\frac{sinx}{cosx}$ , then

tanΘ = $\frac{-\frac{3}{5} }{-\frac{4}{5} }$ = - $\frac{3}{5}$ × - $\frac{5}{4}$ = $\frac{3}{4}$