What are the divisors of 64

The diagram shows how cos θ, sin θ, and tan θ relate to the unit circle. Copy the diagram and show how sec θ, csc θ, and cot θ r

DIA [1.3K]

Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle.

The representation of the diagram is shown if Figure 1. There's a relationship between sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.

a.1 First, find in the diagram a segment whose length is sec θ.

The segment whose length is sec θ is shown in Figure 2, this length is the segment $\overline{OF}$ , that is, the line in green.

a.2 Explain why its length is sec θ.

We know these relationships:

(1) $sin \theta=\frac{\overline{BD}}{\overline{OB}}=\frac{\overline{BD}}{r}=\frac{\overline{BD}}{1}=\overline{BD}$

(2) $cos \theta=\frac{\overline{OD}}{\overline{OB}}=\frac{\overline{OD}}{r}=\frac{\overline{OD}}{1}=\overline{OD}$

(3) $tan \theta=\frac{\overline{FD}}{\overline{OC}}=\frac{\overline{FC}}{r}=\frac{\overline{FC}}{1}=\overline{FC}$

Triangles ΔOFC and ΔOBD are similar, so it is true that:

$\frac{\overline{FC}}{\overline{OF}}= \frac{\overline{BD}}{\overline{OB}}$ 

∴ $\overline{OF}= \frac{\overline{FC}}{\overline{BD}}= \frac{tan \theta}{sin \theta}= \frac{1}{cos \theta} \rightarrow \boxed{sec \theta= \frac{1}{cos \theta}}$ 

b.1 Next, find cot θ

The segment whose length is cot θ is shown in Figure 3, this length is the segment $\overline{AR}$ , that is, the line in pink.

b.2 Use the representation of tangent as a clue for what to show for cotangent.

It's true that:

$\frac{\overline{OS}}{\overline{OC}}= \frac{\overline{SR}}{\overline{FC}}$

But:

$\overline{SR}=\overline{OA}$
$\overline{OS}=\overline{AR}$

Then:

$\overline{AR}= \frac{1}{\overline{FC}}= \frac{1}{tan\theta} \rightarrow \boxed{cot \theta= \frac{1}{tan \theta}}$

b.3 Justify your claim for cot θ.

As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:

$cot \theta= \frac{\overline{AR}}{\overline{OA}}=\frac{\overline{AR}}{r}=\frac{\overline{AR}}{1} \rightarrow \boxed{cot \theta=\overline{AR}}$

c. find csc θ in your diagram.

The segment whose length is csc θ is shown in Figure 4, this length is the segment $\overline{OR}$ , that is, the line in green.

3 0

4 years ago

Amelia need 1/2 stick of butter to make cornbread he also needs one fourths stick butter to make apple muffins what fraction of

Viktor [21]

Amelia needs $\frac{3}{4}$ stick of butter to make cornbread and apple muffins.

Step-by-step explanation:

Given,

Stick of butter needed to make cornbread = $\frac{1}{2}$

Stick of butter needed to make apple muffins = $\frac{1}{4}$

Total stick of butter needed = Cornbread + Muffins

Total stick of butter needed = $\frac{1}{2}+\frac{1}{4}$

Total stick of butter needed = $\frac{2+1}{4}$

Total stick of butter needed = $\frac{3}{4}$

Amelia needs $\frac{3}{4}$ stick of butter to make cornbread and apple muffins.

Keywords: fraction, addition

Learn more about addition at:

#LearnwithBrainly

6 0

3 years ago

Find the area of the shaded region of the trapezoid.

BigorU [14]

Area of entire trapezoid = ((sum of the bases) ÷ 2) • height
Trapezoid Area = (51 / 2) * 26
Trapezoid Area = 663

UN-shaded triangle area = .5 * base * height
UN-shaded triangle area = .5 * 23 * 26
UN-shaded triangle area = 299

SHADED Trapezoid Area = 663 -299
SHADED Trapezoid Area = 364

3 0

3 years ago

Write the equation in the point slope form for the line that contains the points (-2,-3), (4,3)

Marina86 [1]

Answer:

Answer is 4 I think!!

4 0

3 years ago

Read 2 more answers

bejamin writes an expresssion for the sum of 1 cubed 2 cubed and 3 cubed what is the value of the expresssion

sashaice [31]

Answer:

36

Step-by-step explanation:

1^3 + 2^3 + 3^3 = 1 + 8 + 27 = 36

5 0

3 years ago