What's 70x 9/10 show work
2 answers:
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How I was taught all of these problems is in terms of r, x, and y. Where sin = y/r, cos = x/r, tan = y/x, csc = r/y, sec = r/x, cot = x/y. That is how I will designate all of the specific pieces in each problem.
#3
Let's start with sin here. Therefore, because sin is y/r, r =
and y = +2. Moving over to cot, which is x/y, x = -1, and y = 2. We know y has to be positive because it is positive in our given value of sin. Now, to find cos, we have to do x/r.
cos =
#4
Let's start with secant here. Secant is r/x, where r (the length value/hypotenuse) cannot be negative. So, r = 9 and x = -7. Moving over to tan, x must still equal -7, and y = . Now, to find csc, we have to do r/y.
csc =
The pythagorean identities are
sin^2 + cos^2 = 1,
1 + cot^2 = csc^2,
tan^2 + 1 = sec^2.
#5
Let's take a look at the information given here. We know that cos = -3/4, and sin (the y value), must be greater than 0. To find sin, we can use the first pythagorean identity.
sin^2 + (-3/4)^2 = 1
sin^2 + 9/16 = 1
sin^2 = 7/16
sin = =
Now to find tan using a pythagorean identity, we'll first need to find sec. sec is the inverse/reciprocal of cos, so therefore sec = -4/3. Now, we can use the third trigonometric identity to find tan, just as we did for sin. And, since we know that our y value is positive, and our x value is negative, tan will be negative.
tan^2 + 1 = (-4/3)^2
tan^2 + 1 = 16/9
tan^2 = 7/9
tan = -
#6
Let's take a look at the information given here. If we know that csc is negative, then our y value must also be negative (r will never be negative). So, if cot must be positive, then our x value must also be negative (a negative divided by a negative makes a positive). Let's use the second pythagorean identity to solve for cot.
1 + cot^2 =
1 + cot^2 = 6/4
cot^2 = 2/4
cot =
tan =
Next, we can use the third trigonometric identity to solve for sec. Remember that we can get tan from cot, and cos from sec. And, from what we determined in the beginning, sec/cos will be negative.
+ 1 = sec^2
4/2 + 1 = sec^2
2 + 1 = sec^2
sec^2 = 3
sec = -
cos =
Hope this helps!! :)
Answer:
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x-y-(4)=0
Step 1:
Equation of a Straight Line
Solve 2x-y-4 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 2x-y-4 = 0 and calculate its properties
Graph of a Straight Line :
( see attatchment)
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 4/-1 so this line "cuts" the y axis at y=-4.00000
y-intercept = 4/-1 = -4.00000
Calculate the X-Intercept :
When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000
x-intercept = 4/2 = 2
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -4.000 and for x=2.000, the value of y is 0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.000 - (-4.000) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2
Geometric figure: Straight Line
1. Slope = 2
2. x-intercept = 4/2 = 2
3. y-intercept = 4/-1 = -4.00000
- clarification for graph - green means rise red means run , bottom black is x intercept which is 2.000 under rise is y-intercept and under the y axis is 0.000 and -4.000.
