Question

if tan theta=5/12 find sin² theta and cos² theta​

Answer 1

Answer:

sin^2 theta = 25/169 cos^2 theta = 144/19

Step-by-step explanation:

tan theta = 5/12

tan theta = opposite/adjacent

hence, opposite = 5, adjacent = 12

hypotenuse = ?

hypo^2 = oppo^2 + adjacent^2

hypo^2 = 5^2 + 12^2 = 25+ 144=169

hypo^2 = 169

hypotenuse = 13

sin theta = opposite/ hypotenuse

sin^2 theta = (5/13)^2 = 25/169

cos theta = adjacent / hypotenuse

cos^2 theta = (12/13)^2 = 144/169

Answer 2

Answer:

sin^2 theta=25/169,cos^2 theta=144/169

Step-by-step explanation:tan theta=5/12=opposite/adjacentin the triangle, by the pythagoras therom

opposite^2+adjacent^2=hypotenuse^2

5^2+12^2=h^2

25+144=h^2

h^2=169

h=root169

=root (13)^2=13

sin^2 theta=opposite^2/hypotenuse^2=5^2/13^2=25/169

cos^2 theta=adjacent^2/hypotenuse^2=12^2/13^2=144/169

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