Plz Solve Will Mark Brainliest and No Stealing Points Or Will Report Part 2
1 answer:
Answer:
Before we graph we know that the slope, mx, could be read as
. To graph the the equation of the line, we begin at the point (0,0). From that point, because our rise is negative (-1), instead of moving upwards or vertically, we will move downards. Therefore, from point 0, we will vertically move downwards one time. Now, our point is on point -1 on the y-axis. Now, we have 2 as our run. From point -1, we move to the right two times. We land on point (2,-1). Because we need various points to graph this equation, we must continue on. In the end, the graph will look like the first graph given.
For the equation y = 2, the line will be plainly horizontal. Why? Because x has no value in the equation. The variable does not exist in this linear equation. Therefore, it will look like the second graph below. We graph this by plotting the point, (0,2), on the y-axis.
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Answer:
a) Third Quadrant
b) 7π/4 --> Option (4)
c) --> Option (1)
d) 1 --> Option (1)
e) --> Option (2)
f) - --> Option (2)
g) --> Option (1)
h) --> Option(2)
Step-by-step explanation:
Ok, lets properly define some technical term here.
The terminal side of an angle is the side of the line after that it has made a turn (angle). I will drive my point home with the attachment to this solution
The initial side of an angle is the side of the line before the line made a turn(angle)
a) 1 complete revolution = = 2π rads
we can convert the radians to degrees using the above conversion rate
=> will be:
solving the expression above, 420π/2π =
From the value of the angle in degree and having in mind that
b) Co-terminal angles are angles which share the same initial and terminal side
To find the co-terminal of an angle we add or subtract 360 to the value if in degrees or 2π if in radians. From the value we want to find its co-terminal, because of the presence of π, its value is in radians and as such we add or subtract 2π from the value. If we perform subtraction, the negative co-terminal of the angle has been evaluated and the positive co-terminal is evaluated if we perform addition.
So, to get the positive co-terminal of -π/4, we add 2π and doing that, we get:
2π - π/4 = 7π/4
c) The value of sin(π/3) * cos(π) is ?
Applying special angle properties: (More on the special angle in the diagram attached to this solution)
sin(π/3) =
cos(π) = -1
substituting the values above into the expression, we have:
d) if , f(π/4) = ?
In trignometry,
Applying special angle properties again,
sin(π/4) =
cos(π/4) =
The expression becomes . Simplifying, we get:
2/4 + 2/4 = 1/2 + 1/2 = 1
e) cos(3π/4)
3π/4 is not an acute angle(angle < less than π/2 rad) and as such, we need to get its related acute angle. Now 3π/4 rads is in the second quadrant, this means that we will have to subtract 3π/4 from π to get the related acute angle.
π - 3π/4 = π/4
so instead of working with 3π/4, we work with its related acute angle which is π/4
cos(3π/4) is equivalent to cos(π/4) = (special angle properties)
f) sin(11π/6)
11π/6 is not an acute angle(angle less than π/2 rad) and it is in the fourth quadrant. This means that to get its related acute angle, we have to subtract it from 2π
2π - 11π/6 = π/6
sin(11π/6) is equivalent to -sin(π/6) = -1/2 (special angle properties).
Note that there is a minus in the answer. That had nothing to do with the special angle properties but rather, the fact that:
- At the fourth quadrant, only the cosine trignometric ratio is positive
- At the first quadrant, all trignometric ratios are positive
- At the second quadrant, only the sine trignometric ratio is positive
- At the third quadrant, only the tangent trignometric ratio is positive
g) sin(π/6) + tan(π/4)
using special angle properties:
sin(π/6) = 1/2 and tan(π/4) = 1
the expression simplifies to: 1/2+1 = 3/2
h) cos(4π/3)
4π/3 is not an acute angle and it is in the third quadrant
To get its related acute angle, we have to subtract it from 3π/2
3π/2 - 4π/3 = π/6
so, cos(4π/3) = -cos(π/6) (The negative value is because of the fact that at the third quadrant, only the tangent trignometric ratio is positive)
using special angle properties, -cos(π/6) =
