If sin (x+20°)=cos x. Find the value of x.
1 answer:
Sin(90-x)=cos(x), so 90-x=x+20. Solve for x:
90-x=x+20
70=2x
x=35 degrees.
Proof for the identity, sin(90-x)=cos(x):
Recall the following formulas:
These sides are relative to the same reference angle, x. If you use the angle 90-x instead, then a few things change. The hypotenuse does not change, because the two triangles will share that side. Because the triangles are both right triangles, if they share the same hypotenuse, then they will form a rectangle. A rectangle has equal opposite sides. This is illustrated clearly in the attached image.
The side that was opposite of the angle x is the same length as the side that is adjacent to the angle 90-x, and the side that was adjacent to the angle x is the same length as the side that is opposite of the angle 90-x. So, if you have cos(x), it is the side adjacent to the angle x divided by the hypotenuse. The side adjacent of the angle x is equal to the side opposite of the angle 90-x. So cos(x) is also equal to the side opposite of the angle 90-x divided by the hypotenuse. Does this sound familiar? It is the trig function for sine. So sin(90-x)=cos(x).
90-x=x+20
70=2x
x=35 degrees.
Proof for the identity, sin(90-x)=cos(x):
Recall the following formulas:
These sides are relative to the same reference angle, x. If you use the angle 90-x instead, then a few things change. The hypotenuse does not change, because the two triangles will share that side. Because the triangles are both right triangles, if they share the same hypotenuse, then they will form a rectangle. A rectangle has equal opposite sides. This is illustrated clearly in the attached image.
The side that was opposite of the angle x is the same length as the side that is adjacent to the angle 90-x, and the side that was adjacent to the angle x is the same length as the side that is opposite of the angle 90-x. So, if you have cos(x), it is the side adjacent to the angle x divided by the hypotenuse. The side adjacent of the angle x is equal to the side opposite of the angle 90-x. So cos(x) is also equal to the side opposite of the angle 90-x divided by the hypotenuse. Does this sound familiar? It is the trig function for sine. So sin(90-x)=cos(x).
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Answer:
The table is show clearly in the figure attached.
P(boy if favourite activity is swimming) = 8/17 = 0.47
P(girl if favourite activity is sport) = 7/27 = 0.26
P(girl if favourite activity is reading) = 4/6 = 0.67
P(boy if favourite activity is sport) = 20/27 = 0.74
P(favourite activity is swimming if a girl) = 9/20 = 0.45
P(favourite activity is reading if a boy) = 2/30 = 0.07
P(favourite activity is swimming if a boy) = 8/30 = 0.27
P(favourite activity is reading if a girl) = 4/20 = 0.2
The constant of proportionality is equal to 11.
<h3>Constant of Proportionality</h3>The constant of proportionality is the ratio that relates two given values in what is known as a proportional relationship. Other names for the constant of proportionality include the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
In this question, the constant of proportionality is that value that doesn't change or represents the number of players while x represented the number of games they played.
The constant of proportionality can be solved mathematically as
The constant of proportionality is the value that makes y = 11x and it is 11.
Learn more on proportionality here;
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