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

Using ur calculator you should get 15 degrees ( Use the sin-1 key.).

Angle complementary to x is 90-15 = 75 degrees

and as sin x = cos(90-x) then cos 75 is also equal 0.2588

Answer 2

Answer: 1) The approximate value of x is 15°,

2) The approximate value of cosine of the angle that is complementary to x is 0.2588.

Explanation:

1) According to the question,

`sin x = 0.2588`

`\implies x = sin^(-1)(0.2588)`

`\implies x = 14.9988703055\approx 15^(\circ)`

2) Now, the complementary of x = 90° - x = 90° - 15° = 75°

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

cos (75°) = 0.2588190451 ≈ 0.2588

Note : The two angles are complementary angles if their sum is 90°.