If sin theta equal to 24 by 25 then find the value of sin square theta + cos square theta
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Given,
sin θ = 24/25
θ lies in the second quadrant.
In the second quadrant sec and tan are negative.
sin θ = 24/25 = Opp/Hyp
By Pythagoras theorem,
(Hyp)2 = (Opp)2 + (Adj)2
(25)2 = (24)2 + (x)2
x2 = 625 – 576
x2 = 49
x = 7
tan θ = Opp/Adj = -24/7 {quadrant II}
sec θ = Hyp/Adj = -25/7 (quadrant II}
sec θ + tan θ = (-24/7) + (-25/7)
= -49/7
= -7
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