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The thing that looks like the hypotenuse of a right triangle is called a vector . It has a length and it has a direction. Typically, the direction is stated as the angle between the vector and the horizontal axis. Thus, thedirection is analogous to the angle at the origin in the triangle on your graph board.

Horizontal and vertical components

For reasons that I won't explain until we get to that module, you will often need to compute the horizontal and vertical components of the vector.The horizontal component is essentially the adjacent side of our current right triangle. Thus, the value of the horizontal component can be computed using thesecond equation in Figure 10 .

The vertical component is essentially the opposite side of our current right triangle, and its value can be computed using the first equation in Figure 10 .

The tangent and arctangent of an angle

Once again, although the tangent of an angle is based on very specific geometric considerations involving circles (see (External Link) ), for our purposes, the tangent of an angle is simply a ratio between the lengths of two different sides of a righttriangle.

A ratio of two sides

For our purposes, we will say that the tangent of an angle is equal to the ratio of the opposite side and the adjacent side. Therefore, in the case of the3-4-5 triangle that you have on your graph board, the tangent of the angle at the origin is equal to 4/3 or 1.333.

Not limited to 1.0

Note that the absolute value for the sine and the cosine of an angle is limited to a maximum value of 1.0. However, the tangent of an angle is not solimited. In fact, the tangent of 45 degrees is 1.0 and the tangent of 90 degrees is infinity. This results from the length of the adjacent side, which is thedenominator in the ratio, going to zero at 90 degrees.

Dividing by zero in a script is usually not a good thing. This is a pitfall that you must watch out for when working with tangents. I will provide code later on that shows you how deal with this issue.

Computing the tangent

If we know the lengths of the opposite side and the adjacent side, we can compute the tangent and use it for other purposes later without having to knowthe value of the angle.

Conversely, if we know the value of the angle but don't know the lengths of the adjacent side and/or the opposite side, we can obtain the tangent valueusing a scientific calculator or lookup table and use it for other purposes later.

The tangent of an angle -- sample computation

Enter the following into the Google search box:

tan(53.13010235415598 degrees)

The following will appear immediately below the search box:

tan(53.13010235415598 degrees) = 1.33333333

This agrees with the ratio that we computed earlier .

The arctangent (inverse tangent) of an angle

The arctangent of an angle is the value of the angle having a given tangent value. (For example, as mentioned above, the arctangent of infinity is 90degrees and the arctangent of 1.0 is 45 degrees.) In other words, if you know the value of the tangent of an unknown angle, you can use a scientific calculator or lookup table to find the value of theangle.

Questions & Answers

explain and give four Example hyperbolic function
Lukman Reply
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
SABAL Reply
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?
mariel Reply
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?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
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
Only Reply
how do we prove the quadratic formular
Seidu Reply
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Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
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Seidu
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Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
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
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-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
Alfred Reply
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.
Kimberly Reply
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.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
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)=
Crystal Reply
. 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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Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
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