Question

if sin theta = -3/5 and theta lies in the third quadrant , find tan theta and sec theta.​

Answer 1

Answer:

tan theta is -3 / -4

sec theta is -4/5

Step-by-step explanation:

hope its help

Answer 2

Given:

sin theta = -3/5 and theta lies in the third quadrant

To find:

if sin theta = -3/5 and theta lies in the third quadrant , find tan theta and sec theta.​

Solution:

From given, we have,

sin theta = -3/5 and theta lies in the third quadrant

we use the trigonometric ratios and trigonometric formulae.

sin ²theta + cos ²theta = 1

(-3/5)² + cos ²theta = 1

9/25 + cos ²theta = 1

cos ²theta = 1 - 9/25

cos ²theta = 16/25

cos theta = 4/5

Now consider,

tan theta = sin theta / cos theta

= (-3/5) / (4/5)

= - 3/4

sec theta = 1 / cos theta

= 1 / (4/5)

= 5/4

The values of tan theta and sec theta are -3/4 and 5/4