please draw the unit circle as well 2528 Values of Trigonome

please draw the unit circle as well.

25-28 Values of Trigonometric Functions Find the values of the trigonometric function of t from the given information. 25. sec t cot t: tan r i, terminal point for t in Quadrant III

Solution

tan t=1/4

In third quadrant cosine is negative

here opposite=1   and adjacent=4

hypotenuse=sqrt(1²+4²) = sqrt17

cos t= -4/sqrt17

sec t=1/cos t=-sqrt17/4

cot t=1/tan t=4/1

sec t + cot t= -sqrt17 /4   + 4/1 = (16 - sqrt17)/4