Question

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

Answer 1

Answer:
`\bold{\cot\theta=-(5)/(12)\qquad \sec\theta = (13)/(5)\qquad \cos\theta = (5)/(13)}`

Explanation:

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

`\cos \theta = (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=(x)/(y)\quad =(5)/(-12)\quad =\large\boxed{-(5)/(12)}\\\\\\\sec\theta=(r)/(x)\quad = (13)/(5)\quad = \large\boxed{(13)/(5)}\\\\\\\cos\theta =(5)/(13)\quad \text{(Given)}\\`