Question

given that tan theta = 5/12 and theta is acute angle , find sin theta and cos theta.

Answer 1

Answer:

sin theta = 5/13

cos theta = 12/3

Step-by-step explanation:

tan theta = 5/12

sec2 theta = 1 + tan2 theta

                  = 1 + 25/144 = 144+25/144 = 169/144

sec theta = 13/12

cos theta = 1/ sec theta = 12/13

cos2 theta + sin2 theta =1

sin2 theta = 1- cos2 theta

                = 1- 144/169 = 169-144/169 = 25/169

sin theta = root of 25/ 169 = 5/13

Answer 2

Answer:

1 + tan^2 theta = sec^2 theta

1 + (5/12)^2 = sec^2 theta

1 + 25/144 = sec^2 theta

(144+25)/144 = sec^2 theta

169/144 = sec^2 theta

sec theta = +/- 13/12

sec theta = 13/12 (theta is an acute angle. It lies in the first quadrant. All ratios are positive)

sec theta = 1/cos theta

cos theta = 1/sec theta

cos theta = 1/13/12

cos theta = 12/13

sin^2 theta + cos^2 theta = 1

sin^2 theta = 1 - cos^2 theta

sin^2 theta = 1 - (12/13)^2

sin^2 theta = 1 - 144/169

sin^2 theta = (169 - 144)/169

sin^2 theta = 25/169

sin theta = +/- 5/13

sin theta = 5/13 (Reason same as above)