1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sattari [20]
3 years ago
11

Find sin 2x, cos 2x, and tan 2x from the given information. cscx=4,tanx<0.

Mathematics
1 answer:
lutik1710 [3]3 years ago
5 0

Answer:

Step-by-step explanation:

Given the expression cosec (x) = 4 and tan(x)< 0

since cosec x = 1/sinx

1/sinx = 4

sinx = 1/4

From SOH, CAH TOA

sinθ = opposite/hypotenuse

from sinx = 1/4

opposite = 1 and hypotenuse = 4

to get the adjacent, we will use the Pythagoras theorem

adj² = 4²-1²

adj² = 16-1

adj ²= 15

adj = √15

cosx = adj/hyp = √15/4

tanx = opposite/adjacent = 1/√15

since tan < 0, then tanx = -1/√15

From double angle formula;

sin2x = 2sinxcosx

sin2x = 2(1/4)(√15/4)

sin2x = 2√15/16

sin2x = √15/8

for cos2x;

cos2x = 1-2sin²x

cos2x = 1-2(1/4)²

cos2x = 1-2(1/16)

cos2x= 1-1/8

cos2x = 7/8

for tan2x;

tan2x  = tanx + tanx/1-tan²x

tan2x = 2tanx/1-tan²x

tan2x = 2(-1/√15)/1-(-1/√15)²

tan2x = (-2/√15)/(1-1/15)

tan2x = (-2/√15)/(14/15)

tan2x = -2/√15 * 15/14

tan2x = -30/14√15

tan2x = -30/7√15

rationalize

tan2x =  -30/7√15 * √15/√15

tan2x =  -30√15/7*15

tan2x =  -2√15/7

You might be interested in
A glider plane travels 120 miles in 2 hours. At that rate, how many hours will it take the plane to travel 300 miles?
tigry1 [53]

The answer is C.........

3 0
3 years ago
What is the resulting ordered pair if the value of the independent variable is 5?
eduard
F(5) = -2 * 5 + 1 = -9
the pair is (5, -9)
6 0
3 years ago
Grocery store sells tangerines in 2/5 kg bags. A customer bought 4kg of tangerines for a school party. How many bags did he buy
Rama09 [41]

In order to have 4 kg, he must have 20/5 kg. Each bag is 2/5 kg, so 2/5 times 10 is 20/5 or 4kg. Therefore, he bought 10 bags of tangerines for the school party.

6 0
3 years ago
In Roman Numerals, a bar means to multiply that number by 1000. What is 99 004 in roman numerals?
klemol [59]
I’m pretty sure it’s XCIX IV I hope this helped
8 0
2 years ago
The temperature of a liquid in an experiment is at 0 degrees Celsius at 9 am. The experiment calls for the temperature to drop 1
RSB [31]

Answer:

don't know don't know don't know don't know don't know don't know don't know

Step-by-step explanation:

don't know don't know don't know don't know don't know don't know don't know don't know

8 0
2 years ago
Other questions:
  • Use ΔABC below to answer the question that follows:
    15·2 answers
  • What’s the answer please hurry up
    5·2 answers
  • Find the area of a trapezoid please help im so lost
    9·1 answer
  • 2=n over 3 what does n equal?
    12·2 answers
  • 化學製程中溫度的影響 為研究化學製程中溫度對產量之影響,我們在 3 種溫度下各生產 3批產品,結果如下表。請建立 ANOVA 表。在 0.05 顯著水準檢定不同的溫度是否會影響平均產量。
    12·1 answer
  • Select all sets in which the number
    7·1 answer
  • Becky received a statement on her Certificate of Deposit showing that her investment had returned $6,336 over its life. If the C
    10·1 answer
  • Multiply 5/8⋅4/5.<br> Simplify the answer, if possible. <br> 9/13 <br> 1 1/740 <br> 20/40 <br> 1/2
    13·1 answer
  • An auditorium has a seating capacity of 1500. For an upcoming event community event theater play, tickets cost $4 for adults and
    10·1 answer
  • Handedness: 18 left-handed
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!