Question

i need help with 3 (along with 3a-c) i am confused on what to do with the numbers that are in degrees...

Answer 1

Answer:

$\frac{5}{128}$ = 0.03906

Step-by-step explanation:

The confusing part is the fact that you have "pure" numbers and degrees i guess right?

In maths we differ two ways to measure angles:

Degrees and Radians. Degrees are always given with the degree-symbol °. Meanwhile the radians are "pure" numbers, if you want to call it that. They are mostly given in relation to pi, e.g. $\frac{\pi}{2}$ ≈ 1.57079 in radians correspond to a 90° angle.

In your task you are probably expected to use your calculator. For cosine and sine functions it is really important to differ whether the number you are giving the function is in radians or degrees. To tell your calculator whether you are using degree or radian as "units" for the angle you input in cosine and sine functions, you use the rad/deg button.

In your task you would put the calculator to deg, as the angles are given in degrees.

Step-by-Step:

$\frac{cos(36\°)+sin(18 \°)}{\sqrt{29^2 -21.8}}$

= $\frac{cos(\frac{\pi}{5})+ sin(\frac{\pi}{10})}{\sqrt{29^2 -21.8}}$

Now we need to use some Trigonometric Identities:

$cos(\frac{\pi}{5}) = \frac{1}{4}(1 + \sqrt{5})$

$sin(\frac{\pi}{10}) = \frac{1}{4}(\sqrt{5} - 1)$

(See: https://mathworld.wolfram.com/TrigonometryAnglesPi10.html )

So in the numerator we can simplify the two terms:

$(\frac{1}{4}(1 + \sqrt{5}) + \frac{1}{4}(\sqrt{5} - 1) = \frac{1}{4} (1 + \sqrt{5} + \sqrt{5} - 1) = \frac{1}{2} \sqrt{5})$

Ok. Nice.

Now the denumerator:

$\sqrt{29^2 -21.8} = \sqrt{819.2}$

Doesn't seem to help right? Well, if you multiply 819.2 with 5 you get 4096 which is the square of 64. So, we do the following:

$\frac{\frac{1}{2}\sqrt{5}}{\sqrt{819.2}} * \frac{\sqrt{5}}{\sqrt{5}} = \frac{1}{2} * \frac{5}{64} = \frac{5}{128}$

Answer 2

Answer:

The answer to your question is below

Step-by-step explanation:

Let p = $\frac{cos x + siny}{\sqrt{w^{2} - z}}$

x = 36°

y = 18°

w = 29

z = 21.8

- Substitution

p = $\frac{cos 36 - sin 18}{\sqrt{29^{2} - 21.8}}$

- Simplification

p = $\frac{0.809 - 0.309}{\sqrt{841 - 21.8}}$

p = $\frac{0.5}{\sqrt{819.2}}$

p = $\frac{0.5}{28.622}$

a) Result

p = 0.017469281

b) Three significant figures

p = 0.017

c) Scientific notation

p = 1.7 x 10⁻²

a = 1.7   k = -2