Use the fundamental identities to find the value of the trig

Use the fundamental identities to find the value of the trigonometric function. Find cot theta if sec theta - squareroot 29/2 and theta is in quadrant II - 5/2 - squareroot 29/2 2/5 squareroot 29/2

Solution

Sec theta=-sqrt29/5

Cos theta=1/sec theta= -5/sqrt29

Adjacent=5 hypotenuse=sqrt29

Opposite= sqrt((sqrt29)²- 5²) = 2

Theta is in second quadrant and in second quadrant sine is positive

Sin theta= opposite/hypotenuse=2/sqrt29

Cot theta= cos theta/sin theta = -5/2

Correct option is A