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3 years ago

Which is shorter 3/6 of a minute or 2/6 of an hour

Mathematics

2 answers:

kolbaska11 [484]3 years ago

8 0

3/6 of a minute which is 30 seconds

Juliette [100K]3 years ago

6 0

3/6 of a minute because an hour is much longer

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I have to use trigonometric identities to solve. But I’m having trouble finding the values of cos A and sin B. Can anyone help m

katrin [286]

let's notice something, angles α and β are both in the I Quadrant, and on the first quadrant the x-coordinate/cosine and y-coordinate/sine are both positive.

$\bf \textit{Sum and Difference Identities} \\\\ cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin(\alpha)=\cfrac{\stackrel{opposite}{15}}{\stackrel{hypotenuse}{17}}\impliedby \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}$

$\bf \pm\sqrt{17^2-15^2}=a\implies \pm\sqrt{64}=a\implies \pm 8 = a\implies \stackrel{I~Quadrant}{\boxed{+8=a}} \\\\[-0.35em] ~\dotfill\\\\ cos(\beta)=\cfrac{\stackrel{adjacent}{3}}{\stackrel{hypotenuse}{5}}\impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}$

$\bf \pm\sqrt{5^2-3^2}=b\implies \pm\sqrt{16}=b\implies \pm 4=b\implies \stackrel{\textit{I~Quadrant}}{\boxed{+4=b}} \\\\[-0.35em] ~\dotfill$

$\bf cos(\alpha - \beta)=\stackrel{cos(\alpha)}{\left( \cfrac{8}{17} \right)}\stackrel{cos(\beta)}{\left( \cfrac{3}{5} \right)}+\stackrel{sin(\alpha)}{\left( \cfrac{15}{17} \right)}\stackrel{sin(\beta)}{\left( \cfrac{4}{5} \right)}\implies cos(\alpha - \beta)=\cfrac{24}{85}+\cfrac{60}{85} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill cos(\alpha - \beta)=\cfrac{84}{85}~\hfill$

5 0

3 years ago

Igebra 1: CC 2015 > Chapter 1: Rewriting Equations and Formulas > Section Exercises 1.5 > Exercise 33

Ivanshal [37]

Answer:

I LOVE YOU WITH ALL MY HEART

Step-by-step explanation:

6 0

3 years ago

What two numbers create a product of -12 and a sum of 4?

Katen [24]

Answer:

-2 and 6

Step-by-step explanation:

-2+6=4

-2×6=-12

7 0

3 years ago

Read 2 more answers

Corey has 140 marbles. He gives 16 to his younger brother. He divides the rest equally into four bags. How many go in each bag?

madreJ [45]

31 marbles would go into each bag.

8 0

3 years ago

The diameter of a circle is 10 in. Find its area in terms of pie.

kumpel [21]

Answer:

The diameter of the circle = 10 cm

The radius of the circle= 10/2= 5 cm

Step-by-step explanation:

Area of the circle = pi r^2

= pi 5^2

=3.14 *25

= 78.5 cm ^2

7 0

3 years ago