Question

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?

Answer 1

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 2

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