Question

Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin<0

Answer 1

`\sec\theta=-(5)/(4)`

`\tan\theta=(3)/(4)`

Explanation:

Since the sine function and cosine function is negative hence, the angle theta must lie in 3rd quadrant.

In 3rd quadrant, tangent and cot functions are positive.

a)

`\sec\theta=(1)/(\cos\theta)\\\\\sec\theta=(1)/(-4/5)\\\\\sec\theta=-(5)/(4)`

b)

`\tan\theta=√(\sec^2\theta-1)\\\\\tan\theta=√(25/16-1)\\\\\tan\theta=√(9/16)\\\\\tan\theta=(3)/(4)`