# 5.1 Phy1020: brief trigonometry tutorial  (Page 12/20)

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For example, we know that the tangent of the angle at the origin on your graph board is 1.333. From that, we can determine the value of the angle.

The arctangent of an angle -- sample computation

Enter the following into the Google search box:

arctan(4/3) in degrees

The following will appear immediately below the search box:

arctan(4/3) = 53.1301024 degrees

We can also write a JavaScript script to perform the calculation.

Getting the angle for a known tangent value using JavaScript

Please create an html file containing the code shown in Listing 6 and open it in your browser.

Listing 6 . Arctan of 3-4-5 triangle.
```<!-- File JavaScript06.html --><html><body><script language="JavaScript1.3">function toRadians(degrees){ return degrees*Math.PI/180}//end function toRadians //============================================//function toDegrees(radians){ return radians*180/Math.PI}//end function toDegrees //============================================//var opp = 4 var adj = 3var ratio = opp/adj var angRad = Math.atan(ratio)var angDeg = toDegrees(angRad) document.write("radians = " + angRad + "</br>") document.write("degrees = " + angDeg)</script></body></html>```

The output from the script

Once again, when you open this file in your browser, the output shown in Figure 5 should appear in your browser window.

The code in Listing 6 is very similar to the code in Listing 2 . They both describe the same right triangle, so the output should be thesame in both cases.

The code in Listing 2 uses the opposite side and the hypotenuse along with the arcsine to compute the angle. The code in Listing 6 uses the opposite side and the adjacent side along with the arctangent to compute the angle. Otherwise,no further explanation should be required.

Interesting tangent equations

In the spirit of Figure 7 and Figure 8 , Figure 11 provides some interesting equations that deal with the angle, the opposite side, and the adjacent side.Given any two, you can find the third using either the tangent or arctangent.

Figure 11 . Interesting tangent equations.
```tangent(angle) = opp/adj angle = arctangent(opp/adj)opp = tangent(angle) * adj adj = opp/tangent(angle)```

An exercise involving the tangent

Please copy the code from Listing 7 into an html file and open it in your browser.

Listing 7 . Finding the length of the opposite side.
```<!-- File JavaScript07.html --><html><body><script language="JavaScript1.3">function toRadians(degrees){ return degrees*Math.PI/180}//end function toRadians //============================================//function toDegrees(radians){ return radians*180/Math.PI}//end function toDegrees //============================================//var adj = 3 var angDeg = 53.13var angRad = toRadians(angDeg) var tangent = Math.tan(angRad)var opp = adj * tangent document.write("opposite = " + opp + "</br>") adj = opp/tangentdocument.write("adjacent = " + adj + "</br>")</script></body></html>```

When you open your html file in your browser, the output shown in Figure 12 should appear in your browser window. We can see that the values in Figure 12 are correct for our 3-4-5 triangle.

explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Abdullahi
hi mam
Mark
find the value of 2x=32
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
how do we prove the quadratic formular
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
x+2y-z=7
Sidiki
what is the coefficient of -4×
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Jeannette has \$5 and \$10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
What is the expressiin for seven less than four times the number of nickels
How do i figure this problem out.
how do you translate this in Algebraic Expressions
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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