Question

Let theta be an angle in quadrant IV such that sin theta= -5/13 Find the exact values of sec theta and tan theta

Answer 1

13^2-5^2=12^2
Quad 4: sec is positive, tan is negative
sec=1/cos
cos=12/13
sec=13/12
tan=sin/cos
tan=-5/12

Answer 2

Answer:

$sec\theta =\frac{13}{12}\\\\tan\theta =-\frac{5}{12}$

Step-by-step explanation:

We have value of sin θ = -5/13 and angle in quadrant IV .

In quadrant IV cos θ and sec θ are positive all others are negative.

We have

   $sin\theta =-\frac{5}{13}\\\\sin^2\theta+cos^2\theta=1\\\\\left ( -\frac{5}{13}\right )^2+cos^2\theta=1\\\\cos^2\theta =\frac{144}{169}\\\\cos\theta=\frac{12}{13}\\\\sec\theta =\frac{1}{cos\theta }=\frac{13}{12}\\\\tan\theta =\frac{sin\theta}{cos\theta}=\frac{\frac{-5}{13}}{\frac{12}{13}}=-\frac{5}{12}$

$sec\theta =\frac{13}{12}\\\\tan\theta =-\frac{5}{12}$