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If sinθ = 12/13 find the value of 1 + cosθ A. 5...
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if sinθ = 12/13 find the value of 1 + cosθ

A. 5/13

B. 12/13

C. 25/13

D. 18/13

544
peter
peter
Reputation: 2.6K
University of Lagos, Nigeria
04 May 2020
Comments



2 answer(s)
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james_mark
james_m
Reputation: 921
School not set, Nigeria
19 July 2020
0

sinθ = opposite/hypothenus

and

sinθ = 12/13

opposite = 12

hypothenus = 13

from pythagoras theorem, hypothenus2 = opposite2 + adjacent2

adjacent2 = hypothenus2 - opposite2

adjacent = √(hypothenus2 - opposite2)

adjacent = √(132 - 122)

adjacent = √(169 - 144)

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adjacent = √(25)

adjacent = 5

And,

cosθ = adjacent/hypothenus

cosθ = 5/13

Therefore, 1 + cosθ

= 1 + 5/13

= (13 + 5)/13

= 18/13

Ans D


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judziy
judziy
Reputation: 3.0K
University of Benin, Nigeria
13 May 2020
0

Another approach : Using trigonometry identity

From trigonometry identity, sin2θ + cos2θ = 1

cos2θ = 1 - sin2θ

cos2θ = 1 - (12/13)2

cos2θ = 1 - (144/169)

cos2θ = (169 - 144)/169 (After taking the LCM)

cos2θ = 25/169

cosθ = √(25/169)

cosθ = 5/13

Therefore, 1 + cosθ

= 1 + (5/13)

= 18/13

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