The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.
sec(<em>x</em>) = csc(<em>x</em>)
By definition of secant and cosecant,
1/cos(<em>x</em>) = 1/sin(<em>x</em>)
Multiply both sides by sin(<em>x</em>) :
sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)
As long as sin(<em>x</em>) ≠ 0, this reduces to
sin(<em>x</em>)/cos(<em>x</em>) = 1
By definition of tangent,
tan(<em>x</em>) = 1
Solve for <em>x</em> :
<em>x</em> = arctan(1) + <em>nπ</em>
<em>x</em> = <em>π</em>/4 + <em>nπ</em>
(where <em>n</em> is any integer)
In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of
<em>x</em> = <em>π</em>/4 <u>or</u> <em>x</em> = 5<em>π</em>/4
C. 8 inches. I hope I'm not too late
1.) The answer is A. 5+2x = 17. The x in the equation signifies the number of times Steven went to the big slides. The 5 represents the fixed cost of the slide. The total expenditure in the water park is 17 dollars, and the 2 represents the cost of using 1 big slide.
2.) The answer is still letter A. 5 +2x =17.
So if you want to add
we distribute
a(b+c)=ab+ac so
-2(m+n-4)=-2m-2n+8
5(-2m+2n)=-10m+10n
n(m+4n-5)=mn+4n^2-5n
so total we ahve
-2m-2n+8-10m+10n+mn+4n^2-5n
group like terms
4n^2+-2m-10m-2n+10n-5n+mn+8
add like temrs
4n^2-12m+3n+mn+8
