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Answer:
cos θ = 2/3
Step-by-step explanation:
We presume you want the value of the cosine for
sin θ = √5/3 ≈ 0.745356
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There are several possible approaches you can take to this problem.
1) Using the trig identity:
cos = √(1 -sin²)
cos θ = √(1 -(√5/3)²) = √(1 -5/9) = √(4/9)
cos θ = 2/3
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2) Another approach you can take is to use a calculator to find the angle, then use the calculator to find the cosine of the angle.
cos θ = cos(arcsin(√5/3)) = cos(arcsin(0.745356)) = cos(48.19°) ≈ 0.666667
cos θ = 2/3
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3) Yet another approach is to check the answer choices for reasonableness.
You are given sin θ = 0.745356. This is more than 0.707107, the value where sine and cosine are equal, so the cosine value must be less than 0.707. The answer choices are ...
2/3 ≈ 0.667
3/2 . . . greater than 1; not a viable cosine value
2√5/5 ≈ 0.894 . . . too large
√5/2 . . . greater than 1; not a viable cosine value
3√5/5 . . . greater than 1; not a viable cosine value
So, just looking at the values of the offered answer choices, you can choose the correct one. It is the only value with the appropriate magnitude.
cos θ = 2/3
