Question

(11cos287-25sin557 )/sin17

Answer 1

$\displaystyle \frac{11cos287-25sin557}{sin17}= \frac{11cos(270+17)-25sin(540+17)}{sin17}=$
$\displaystyle = \frac{11sin17+25sin17}{sin17}= \frac{36sin17}{sin17}=36$

Answer 2

Before we begin, let's simplify the angles in the expression:

11 cos 287 = 11 cos (287 - 360) = -11 cos 73

25 sin 557 = 25 sin (557 - 360) = 25 sin 197

Using these simplifications, we can rewrite the expression as:

(-11 cos 73 - 25 sin 197) / sin 17

Now, we need to evaluate each trigonometric function. We can use a calculator to do this. Make sure your calculator is in degree mode.

cos 73 ≈ 0.3090 sin 197 ≈ -0.8733 sin 17 ≈ 0.2924

Substituting these values into the expression, we get:

(-11 × 0.3090 - 25 × (-0.8733)) / 0.2924

Simplifying:

= (-3.399 - (-21.833)) / 0.2924

= 18.434

Therefore, (11cos287-25sin557)/sin17 ≈ 18.434.