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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?

Respuesta :

calculista

Answer:

Part 1) [tex]x=15\°[/tex]

Part 2) [tex]cos(75\°)=0.2588[/tex]

Step-by-step explanation:

Part 1) we have

[tex]sin(x)=0.2588[/tex]

using a calculator

[tex]x=sin^{-1}(0.2588)=15\°[/tex]

Part 2)

we know that

If two angles are complementary

[tex]\alpha+\beta=90\°[/tex] ------> complementary angles

then

[tex]cos(\alpha)=sin(\beta)[/tex]

In this problem

we have

[tex]x=15\°[/tex]

The angle complementary to x is equal to

[tex]90\°-15\°=75\°[/tex]

so

[tex]cos(75\°)=sin(15\°)[/tex]

therefore

[tex]cos(75\°)=0.2588[/tex]

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,

[tex]sin x = 0.2588[/tex]

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

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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