Step-by-step explanation:
For this Q, you should draw a triangle to help you with the values.
cos x =
csc x =
tan x = sin x/ cos x
= 1
cot x = 1
sec x =
x = 45 degrees
What is the difference between a relation and a function(will upvote)
1 answer:
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Answer:
( 1/√ 2 , 1/√ 2 ) , ( 1/√ 2 , - 1/√ 2 ), ( -1/√ 2 , 1/√ 2 ) , ( -1/√ 2 , - 1/√ 2 )
y + 1 = - ( x + 2 ) + √ 2 , y + 1 = - ( x + 2 ) - √ 2 , y + 1 = ( x + 2 ) - √ 2
y + 1 = ( x + 2 ) + √ 2 , ( x + 2 )^2 + ( y + 1)^2 = 1
Step-by-step explanation:
Given:
- Four functions to construct a diamond:
y = −x+ √ 2, y = −x− √ 2, y = x+ √ 2, and y = x − √ 2.
Find:
a)Show that the unit circle sits inside this diamond tangentially; i.e. show that the unit circle intersects each of the four lines exactly once.
b)Find the intersection points between the unit circle and each of the four lines.
(c) Construct a diamond shaped region in which the circle of radius 1 centered at (−2, − 1) sits tangentially. Use the techniques of this section to help.
Solution:
- For first part see the attachment.
- The equation of the unit circle is given as follows:
x^2 + y^2 = 1
- To determine points of intersection we have to solve each given function of y with unit circle equation for set of points of intersection:
For: y = −x+ √ 2 , x - √ 2
And: x^2 + y^2 = 1
x^2 + (+/- * (x - √ 2))^2 = 1
x^2 + (x - √ 2)^2 = 1
2x^2 -2√ 2*x + 2 = 1
2x^2 -2√ 2*x + 1 = 0
2[ x^2 - √ 2] + 1 = 0
Complete sqr: (1 - 1/√ 2)^2 = 0
x = 1/√ 2 , x = 1/√ 2
y = -1/√ 2 + √ 2 = 1/√ 2
y = 1/√ 2 - √ 2 = - 1/√ 2
Points are: ( 1/√ 2 , 1/√ 2 ) , ( 1/√ 2 , - 1/√ 2 )
- Using vertical symmetry of unit circle we can also evaluate other intersection points by intuition:
x = - 1/√ 2
y = 1/√ 2 , -1/√ 2
Points are: ( -1/√ 2 , 1/√ 2 ) , ( -1/√ 2 , - 1/√ 2 )
- To determine the function for the rhombus region that would be tangential to unit circle with center at ( - 2 , - 1 ):
- To shift our unit circle from origin to ( - 2 , - 1 ) i.e two units left and 1 unit down.
- For shifts we use the following substitutions:
x = x + 2 ....... 2 units of left shift
y = y + 1 .......... 1 unit of down shift
- Now substitute the above shifting expression in all for functions we have:
y = −x+ √ 2 -----> y + 1 = - ( x + 2 ) + √ 2
y = −x− √ 2 -----> y + 1 = - ( x + 2 ) - √ 2
y = x- √ 2 -------> y + 1 = ( x + 2 ) - √ 2
y = x+ √ 2 ------> y + 1 = ( x + 2 ) + √ 2
x^2 + y^2 = 1 -----> ( x + 2 )^2 + ( y + 1)^2 = 1
- The following diamond shape graph would have the 4 functions as:
y + 1 = - ( x + 2 ) + √ 2 , y + 1 = - ( x + 2 ) - √ 2 , y + 1 = ( x + 2 ) - √ 2
y + 1 = ( x + 2 ) + √ 2 , ( x + 2 )^2 + ( y + 1)^2 = 1
- See attachment for the new sketch.
Answer:
The degree of this polynomial is "8"
Step-by-step explanation:
Recall that the degree of a polynomial is given by the degree of its leading term. Recall as well that the degree of a term is the maximum number of variables that appear in it.
So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.
1) term contains one variable "m" and four variables "n", so a total of five. Then its degree is: 5
2) term contains one variable "m", two variables "n", and five variables "p". that is a total of eight variables. Then its degree is: 8
3) term contains one variable n and one variable p. That is a total of 2. Then its degree is 2.
Based on the analysis above, and the fact that the term with highest degree is that of degree 8, the polynomial has degree 8.