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3 years ago

Given tanTHETA = -2 and pi/2 < THETA < pi; find cos2THETA.

Mathematics

1 answer:

Troyanec [42]3 years ago

6 0

Answer:

D) $-\frac{3}{5}$

Step-by-step explanation:

<u>Given</u>

<u /> $tan\theta=-2,\:\frac{\pi}{2}$

<u>Use identities</u>

<u /> $cos(2\theta)=\frac{1-tan^2\theta}{1+tan^2\theta}\\\\cos(2\theta)=\frac{1-(-2)^2}{1+(-2)^2}\\\\cos(2\theta)=\frac{1-4}{1+4}\\ \\cos(2\theta)=-\frac{3}{5}$

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Reptile [31]

≻───── ⋆✩⋆ ─────≺

Answer:

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3 years ago

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antoniya [11.8K]

Answer:

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1 year ago

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3 years ago

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Read 2 more answers

The average weight of the class of 35 students was 45 KG. with the admission of a new student the average weight came down to 44

melamori03 [73]

The weight of the new student is 27 kg.

Average weight

= total weight ÷total number of students

<h3>1) Define variables</h3>

Let the total weight of the 35 students be y kg and the weight of the new student be x kg.

<h3>2) Find the total weight of the 35 students</h3>

y= 35(45)

y= 1575 kg

<h3>3) Write an expression for average weight of students after the addition of the new student</h3>

New total number of students

= 35 +1

= 36

Total weight

= total weight of 35 students +weight of new students

= y +x

$44.5 = \frac{y + x}{36}$

<h3>4) Substitute the value of y</h3>

$44.5 = \frac{1575 + x}{36}$

<h3>5) Solve for x</h3>

36(44.5)= 1575 +x

1602= x +1575

<em>Subtract 1575 from both sides:</em>

x= 1602 -1575

x= 27

Thus, the weight of the new student is 27 kg.

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3 years ago