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Gre4nikov [31]
2 years ago
8

For questions 1-2, use the Reciprocal and Quotient Identities to find each value.​

Mathematics
1 answer:
11Alexandr11 [23.1K]2 years ago
8 0

By using the reciprocal identity the value   Sin \theta will be  \dfrac{5}{27}{

<h3>What is Reciprocal and Quotient Identities?</h3>

In trigonometry, quotient identities refer to trig identities that are divided by each other.

So here we have

Cosec\theta = \dfrac{27}{5}

Now we have to find the reciprocal identity,

Sin\theta=\dfrac{1}{Cosec\theta}

Sin\theta}=\dfrac{1}{\dfrac{27} { 5} }

Sin\theta=\dfrac{5}{27}

hence by using the reciprocal identity the value   Sin \theta will be  \dfrac{5}{27}{

To know more about Reciprocating identity follow

brainly.com/question/15769816

#SPJ1

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Set up a ratio:

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DanielleElmas [232]

Answer:

1)

A. m arc QRS = 100°

B. m arc QRT = 255°

C. m arc UTS = 180°

D. m arc UTR = 205°

2)

1] The major arc CA = 255°

2] The minor arc AB = 90°

Step-by-step explanation:

In a circle:

  • The measure of an central angle is equal to the measure of its subtended arc
  • The measure of a circle is 360°
  • Any chord divides a circle into two arcs, a minor arc its measure is < 180° and a major arc its measure is > 180°, the sum of the measures of the minor and major arcs is 360°
  • If the measures of the minor and major arcs are equal, then each arc represents a semi-circle

1)

In circle O

A.

∵ m∠QOR = 75°

∵ ∠QOR subtended by arc QR

- By using the 1st note above

∴ m of arc QR = m∠QOR

∴ m of arc QR = 75°

∵ m∠ROS = 25°

∵ ∠ROS subtended by arc RS

∴ m of arc RS = m∠ROS

∴ m of arc RS = 25°

The measure of arc QRS is the sum of the measures of arcs QR and RS

∴ m arc QRS = 75° + 25° = 100°

B.

∵ m∠SOT = 155°

∵ ∠SOT subtended by arc ST

∴ m of arc ST = m∠SOT

∴ m of arc ST = 155°

The measure of arc QRT is the sum of the measures of arcs QR, RS and ST

∴ m arc QRT = 75° + 25° + 155 °= 255°

C.

∵ m∠UOT = 25°

∵ ∠UOT subtended by arc UT

∴ m of arc UT = m∠UOT

∴ m of arc RUT = 25°

The measure of arc UTS is the sum of the measures of arcs UT and TS

∴ m arc UTS = 25° + 155° = 180°

D.

The measure of arc UTR is the sum of the measures of arcs UT, TS and SR

∴ m arc UTR = 25° + 155° + 25 = 205°

2)

1]

∵ The sum of the measures of the minor and major arcs is 360°

∵ m of minor arc AC = 105°

- Subtract 105 from 360° to find the measure of the major arc CA

∴ m of major arc CA = 360° - 105°

∴ m of major arc CA = 255°

2]

∵ m of major arc AB = 270°

- Subtract 270° from 360° to find the measure of the minor arc AB

∴ m of minor arc AB = 360° - 270°

∴ m of minor arc AB = 90°

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I got the answer by setting up a little table of 6 and 4 and got 24.
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