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If $sin θ = 1213$ , then what is the value of $cos θ$ ?

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513

512

1213

135

answer is A.

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Detailed Solution

Given that,

sin θ = 1213

Sine is a ratio of the side opposite to the angle

θ

by Hypotenuse. Then, if k is any positive integer,

sin θ = 12 k 13 k

⇒ Opposite side H y p o t e n u s e = 12 k 13 k

Form a triangle with respect to

θ

with opposite side as AC and hypotenuse AC.
Question Image

By applying Pythagoras theorem, we get,

A C 2 = B C 2 + A B 2 ⇒ 169 k 2 = 144 k 2 + B C 2 ⇒ B C 2 = 169 k 2 − 144 k 2 ⇒ B C 2 = 25 k 2 ⇒ B C = 5 k

Therefore,

cos θ = Adjacent side H y p o t e n u s e ⇒ cos θ = B C A C ⇒ cos θ = 5 k 13 k ⇒ cos θ = 513

Thus, the value of

cos θ

513

.
Hence, option 4 is correct.

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