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
Answer:
Yes
Step-by-step explanation:
yes
5x+7y=105
There are four variants are possible
1. You sold 15 adult tickets
2. You sold 7 student tickets and 10 adult tickets
3. You sold 14 student tickets and 5 adult tickets
4. You sold 21 student tickets.
Answer:
Step-by-step explanation:
The slope of this line is 2 because the rise from one point is 2, and the run is 1. The change in y-value is divided by the change in the x-value which is 2/1, hence, the slope of the line being 2.
The slope of the line perpendicular to the one shown below will be because the slope that will result in a perpendicular line is the negative reciprocal of the original slope.
Answer:
C (x, y) -> (x + 7, y + 8); scale factor = 3
Step-by-step explanation:
The translation can be found by subtracting the coordinates of the original center from those of the center of the image. The scale factor will be the ratio of the radii.
__
<h3>translation</h3>
We note the center coordinates are I(-3, -6) and I'(4, 2). Then the translation is ...
I' -I = (4, 2) -(-3, -6) = (4 +3, 2 +6) = (7, 8)
(x, y) ⇒ (x +7, y +8)
<h3>scale factor</h3>
The radius of each circle can be found by counting the grid squares from the center to the circle. It works best to do this along a horizontal or vertical line.
The radius of circle I is 2; the radius of circle I' is 6. The scale factor is ...
scale factor = 6/2 = 3
