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Example 1

Example 1 – Continued

Solve \(\csc(x)+6 = 1-3\csc(x)\), where \(0\leq x \leq 2\pi\), correct to two decimal places. Verify the solution using graphing technology.

Solution

Example 1 – Continued

Solve \(\csc(x)+6 = 1-3\csc(x)\), where \(0\leq x \leq 2\pi\), correct to two decimal places. Verify the solution using graphing technology.

Solution

Therefore, the roots in the domain \(0\leq x\leq 2\pi\) are approximately \(4.07\) and \(5.36\).

 

Check Your Understanding A

Given that q, state the value(s) of x in ((((u)*(n))*(i))*(t))*(s), (((((((t)*(o))*(l))*(_))*(t))*(e))*(x))*(t), such that $int_lowml(details...) ≤ x ≤ $int_highml(details...).

 

Do not include the unit of measure. Answers are assumed to be in ((((u)*(n))*(i))*(t))*(s). Separate multiple answers with commas. ((((e)*(x))*(t))*(r))*(a)

x = There appears to be a syntax error in the question bank involving the question field of this question. The following error message may help correct the problem:
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Preview  

((f)*(b))*11.0 ((f)*(b))*12.0
((f)*(b))*21.0 ((f)*(b))*22.0
((f)*(b))*31.0 ((f)*(b))*32.0
((f)*(b))*41.0 ((f)*(b))*42.0

The reference angle is ((((((a)*(l))*(p))*(h))*(a))*(m))*(l)≈(((((((((((a)*(l))*(p))*(h))*(a))*(v))*(a))*(l))*(u))*(e))*(m))*(l).

((((((((t)*(r))*(i))*(g))*(_))*(q))*(u))*(a))*(d)

Therefore, for x in the domain $int_lowml(details...)≤x< $int_highml(details...), x= ((((a)*(n))*(s))*(m))*(l).

 

Check Your Understanding B

Given that (q)*(A), state the exact value(s) of x , in ((d)*(e))*(g), such that (((n)*(u))*(m))*1.0 ≤ x ≤ (((n)*(u))*(m))*2.0 .

 

Do not include the unit of measure in the answer. The solutions for  x are assumed to be in ((d)*(e))*(g). Separate multiple solutions with commas. (((((e)*(x))*(t))*(r))*(a))*(A)

x = There appears to be a syntax error in the question bank involving the question field of this question. The following error message may help correct the problem:
null

Preview  

From the special triangle below, we know that ((((((((F)*(B))*(r))*(e))*(f))*(t))*(r))*(i))*(g). Therefore, the reference angle is ((((F)*(B))*(r))*(e))*(f).

$FBimage(details...)

((((((((((F)*(B))*(q))*(u))*(a))*(d))*(_))*(t))*(e))*(x))*(t).

Since (((n)*(u))*(m))*1.0≤x≤(((n)*(u))*(m))*2.0 then (((n)*(u))*(m))*1.0≤ (s)*(t)≤(((n)*(u))*(m))*3.0.

 

Using this information, we have

(s)*(t)$eqA(details...) (((((((((((((((F)*(B))*(q))*(u))*(a))*(d))*(_))*(v))*(a))*(l))*(u))*(e))*(s))*(_))*(m))*(l).

Therefore, x= (((((a)*(n))*(s))*(m))*(l))*(A).

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