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Aleks04 [339]
2 years ago
15

Hello, precalc, need help on finding csc

Mathematics
1 answer:
Ainat [17]2 years ago
3 0

Recall the double angle identity for cosine:

\cos(2x) = \cos^2(x) - \sin^2(x) = 1 - 2 \sin^2(x)

It follows that

\sin^2(x) = \dfrac{1 - \cos(2x)}2 \implies \sin(x) = \pm \sqrt{\dfrac{1-\cos(2x)}2} \implies \csc(x) = \pm \sqrt{\dfrac2{1-\cos(2x)}}

Since 0° < 22° < 90°, we know that sin(22°) must be positive, so csc(22°) is also positive. Let x = 22°; then the closest answer would be C,

\csc(22^\circ) = \sqrt{\dfrac2{1-\cos(44^\circ)}} = \sqrt{\dfrac2{1-\frac5{13}}} = \dfrac{\sqrt{13}}2

but the problem is that none of these claims are true; cot(32°) ≠ 4/3, cos(44°) ≠ 5/13, and csc(22°) ≠ √13/2...

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1000 times greater (1K)
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For the given linear function, what are the slope and y-intercept?
asambeis [7]

Answer:

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.

Step-by-step explanation:

I had this question not to long ago and got it right

4 0
2 years ago
Apr 24,8:28:53 AM<br> Find the 98th term of the arithmetic sequence -10,-8, -6, ...
Nata [24]

Answer: 184

Step-by-step explanation:

The nth term of am arithmetic sequence is calculated as:

Nth term= a+(n-1)d

where a = first term

d = common difference

a = -10

d = -8 -(-10) = -8+10 = 2

98th term= a+(n-1)d

= -10 + (98-1)(2)

= -10 + (97×2)

= -10 + 194

= 184

The 98th term of the arithmetic sequence is 184

6 0
3 years ago
If one person recruits five people and each recruited person recruits 5 more, and so on, 15 cycles; how many people would that b
jek_recluse [69]

Answer:

y=5^x

5^15= 30517578125 people

Step-by-step explanation:

x=# of cycles= 15 cycles

y= #of people recruited = what we're figuring out

Plug in 15 for x in the equation y=5^x

y= 5^15= 30517578125 people

3 0
3 years ago
Q5 Q6.) Find the exact value of the six trigonometric functions of theta.
lilavasa [31]
5y - 2x + 1 = 0.
5y = 2x-1.

y = 2/5 x - 2/5

this tells us that tan(theta) = 2/5
sin(theta)/sqrt(1-sin^2(theta)) = 2/5
x/sqrt(1-x^2)=2/5
x^2/(1-x^2)=4/25
25x^2=4-4x^2
29x^2=4
x^2=4/29
x = -2/sqrt(29) because quadrant III
cos(x) = sqrt(1-4/29) = -5/sqrt(29)


tan(theta)=2/5
cos(theta)=-5/sqrt(29)
sin(theta)=-2/sqrt(29)
cot(theta)=5/2
sec(theta)=-sqrt(29)/5
csc(theta)=-sqrt(29)/2



5 0
3 years ago
Read 2 more answers
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