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nekit [7.7K]
2 years ago
11

Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.

Mathematics
1 answer:
Westkost [7]2 years ago
5 0
First way
arcsin(1/4) means that 1/4 sin of the angle.

sin(α)=1/4
sin²α+cos²α=1
(1/4)²+cos²α=1
cos²α=1-1/16 =15/16
cosα=+/-(√15)/4

<span>Second way
</span>
sin(α)=1/4 =opposite leg/hipotenuse
cos(α)=adjacent leg/hypothenuse
adjacent leg =√(hypotenuse²- Opposite²)=√(16-1)=√15
cosα=+/-√15/4

For one value of sinα, possible 2 values of cosα.

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Step-by-step explanation:

The question us incomplete without the diagram of the cone and it's dimensions as this would enable us get the exact answer.

Find attached the diagram used in solving the solution.

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