Find tan theta if sin theta 13 and theta terminates in Qj F

Find tan theta if sin theta = 1/3 and theta terminates in Qj. Find sec theta if tan theta = 8/15 and theta terminates in Qlll. Find CSC theta if cot theta = -24/7 and theta terminates in QIV. Find sec theta if tan theta = and cos theta

Solution

7). sin =1/3 is in QI (all are positive)

sin^2 +cos^2 =1

(1/3)^2 +cos^2 =1

cos^2 = 1-1/9

cos = sqrt(8)/3

tan = sin/cos

=1/3 / sqrt(8)/3

=1/sqrt(8)

=1/2sqrt(2)

8). tan =8/15 is QIII (only tan and cot are positive)

by sec^2 -tan^2 =1

sec^2 = 1+(8/15)^2

sec^2 =1 +64/225

sec^2 = 289/225

sec = - 17/15

9).

cot =-24/7 is QIV (so cos and sec are positive)

csc^2 -cot^2 =1

csc^2 = 1 +(24/7)^2

csc = - 25/7

10).

tan =-21/20 is in QII

sec^2 - tan^2 =1

sec^2 = 1 +441/400

sec = - 29/20