Question

If cos =5\13 and 90°≤ø≤180,evaluate cotø,secø,cosø​

Answer 1

Answer:  $\bold{\cot\theta=-\dfrac{5}{12}\qquad \sec\theta = \dfrac{13}{5}\qquad \cos\theta = \dfrac{5}{13}}$

Step-by-step explanation:

90° ≤ θ ≤ 180° means that it is in Quadrant II →   x is + ,  y is -

$\cos \theta = \dfrac{5}{13}\quad \rightarrow\quad x = 5, \ r = 13\\\\\\\text{Use Pythagorean Theorem to find y}:\\x^2+y^2=r^2\quad \rightarrow \quad 5^2+y^2=13^2\quad \rightarrow \quad y = -12\\\\\\\cot\theta=\dfrac{x}{y}\quad =\dfrac{5}{-12}\quad =\large\boxed{-\dfrac{5}{12}}\\\\\\\sec\theta=\dfrac{r}{x}\quad = \dfrac{13}{5}\quad = \large\boxed{\dfrac{13}{5}}\\\\\\\cos\theta =\dfrac{5}{13}\quad \text{(Given)}$