Solution:
As we know reference angle is smallest angle between terminal side and X axis.
As cosine 45 ° is always positive in first and fourth quadrant.
i.e CosФ, Cos (-Ф) or Cos(2π - Ф) have same value.
As, Cos 45°, Cos (-45°) or Cos ( 360° - 45°)= Cos 315°are same.
So, Angles that share the same Cosine value as Cos 45° have same terminal sides will be in Quadrant IV having value Either Cos (-45°) or Cos (315°).
Also, Cos 45° = Sin 45° or Sin 135° i.e terminal side in first Quadrant or second Quadrant.
Answer:
In step A, you replace all trigonometric functions with their definitions in terms of sine and cosine.
In step B, you add the two together as you add fractions.
In step C, you replace 1 with the sum of the squares of sine and cosine.
In step D, you add the cosine terms together so they disappear.
In step E, finally, you divide numerator and denominator by .
Answer:
The amplitude is
Step-by-step explanation:
Let f(x) be a sinusoid function that has the following format:
Then b is the amplitude of the function
h is the vertical displacement of the wave
s is the phase angle
is the period.
In this problem
Then
Therefore the amplitude of the function is
The amplitude is a measure of the vertical size of the sinx wave
Answer:
48 kg
Step-by-step explanation:
The given relations can be used to write a system of equations for the two weights. Those can be solved to find Jane's weight.
__
<h3>setup</h3>Let x and y represent Jane's and Jessica's original weight, respectively. The ratio of weights was ...
x/y = 8/9
After the changes in weight, they were equal:
x+2 = y-4
__
<h3>solution</h3>Adding 4 to the second equation, we have an expression for y that can be substituted into the first equation.
y = x +6 . . . . . . . . . . solve the second equation for y
x/(x+6) = 8/9 . . . . . . substitute for y in the first equation
9x = 8(x +6) . . . . . . . multiply by 9(x+6)
x = 48 . . . . . . . . . . . simplify and subtract 8x
Jane weighed 48 kg at first.
_____
<em>Alternate solution</em>
The original difference in "ratio units" was 9-8 = 1 ratio unit. We find that this corresponds to 6 kg after the weight changes make the weights equal. Then 8 ratio units will be 8(6 kg) = 48 kg—Jane's original weight.
(This mental solution is virtually the same as the solution using equations shown above.)
