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If sinx is approximately 0.2588, what is the measurement of x to the nearest degree? Approximately, what is the cosine of the angle that is complementary to x?

Verified Answer :

calculista

Answer:

Part 1) \(x=15\°\)

Part 2) \(cos(75\°)=0.2588\)

Step-by-step explanation:

Part 1) we have

\(sin(x)=0.2588\)

using a calculator

\(x=sin^{-1}(0.2588)=15\°\)

Part 2)

we know that

If two angles are complementary

\(\alpha+\beta=90\°\) ------> complementary angles

then

\(cos(\alpha)=sin(\beta)\)

In this problem

we have

\(x=15\°\)

The angle complementary to x is equal to

\(90\°-15\°=75\°\)

so

\(cos(75\°)=sin(15\°)\)

therefore

\(cos(75\°)=0.2588\)

Answer:

The value of x is 15°,

The cosine of the angle that is complementary to x is 0.2588(approx)

Step-by-step explanation:

Given,

\(sin x = 0.2588\)

\(\implies x = sin^{-1}(0.2588)= 14.9988703055\approx 15^{\circ}\)

Hence, the value of x is 15°,

Now, the complementary angles are the two angles who give the sum of 90°,

⇒ Complementary angle of x = 90° - x = 90° - 15° = 75°

Thus, the cosine of the angle that is complementary to x,

cos(90-x) = cos 75° = 0.2588190451 ≈ 0.2588

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