 Trigonometric Functions

Decent Essays
Inverse Functions of Trigonometric Functions

As high schoolers go their their teenage years of high school they learn from a variety of subjects. From math to science to history, there is a depth of knowledge to be learned. For math 3 and math 4, we are introduced to the world of trigonometry. So far, we have learned that there are currently three main trigonometric functions, cosine, sine, and tangent. But today I want to explore the other side of the trigonometric world, the inverse functions of cosine, sine, and tangent.

For the first inverse function, cosine, we know that it is obviously the inverse of cosine. The cosine function uses a angle of a right triangle and gives use the ratio of the x-value and the r-value (“Trig Functions:
But instead of tracking the x-value of our unit circle, shown in Figure 1, we track the y-value. This is because the function of sine used the angle of the right triangle but instead of giving us the ratio of the x-value and r-value, it gives us the y-value and r-value (“Trig Functions: Overview”). When we graph the parent function of sine, which is sinx, we get the graph in Figure 4. It look the same as cosine but is shifted the right by 90 degrees. So our roots will be -360, -180, 0, 180, 360 and so on. However, our range is at [1,-1] the same as cosine. For the inverse function of sine, it is the same scenario, shown in Figure 5. The graph is just shifted up 90 degrees from the inverse function of cosine. The x limit is the same scenario too. The period for this function is just different because the distance from the vertex are at a different …show more content…
For this function I want to find a way to be able to graph functions or inverse functions that is technically not a function, so there will be multiple y values for a x value. Constantly, teachers ask students to graph the inverse functions with and without a x-limit. In the more advance concepts of math, students need to have the ability to graph these inverse functions quickly. To do this, I am going to contact the company that makes the most popular graphing calculators, the Texas Instruments Company. I am going to propose them my idea for the ability to reprogram their newest graphing calculator, the TI-84. Then I am going to contact a programing company, Manta, to have them reprogram the calculator for what I want it to do. But first I have to find a way to graph these functions. For this I want to have a new interface for the inverse functions, just like the interface for the functions on the TI-84. To graph the function on the calculator, I want to be able to take the function and make it into the inverse function graph by switch the x-value and y-value at every point. This is because this is what algebraically happens between functions and its inverse function. Then I want it to graph the new coordinates it received, so it will show the user the inverse function. By doing this process and ignoring the function algebraically, I will get a inverse function without a x-limit,

Related Documents

• Decent Essays

However, the lines AB and BC intersect to form a perpendicular angel, and we will use line AC as Ahmed’s route. The end state of the line segments if one was to draw them out would equal a triangle. With the face that Vanessa had turned in a 90 degree angle that makes this triangle a right angle ABC. Lines AB and BC are to be considered as the legs and we will think of AC as the…

• 1157 Words
• 5 Pages
Decent Essays
• Decent Essays

This value was 0.67 error bars away from the estimated value of (19.5 ± 0.5) cm. Another result that can be obtained from the graph is the gradient. The expected gradient was -1 as can be seen in the above picture the gradient from the results was (-1.01 ± 0.02). This shows that the experiment is valid and performed accurately. The second part of the experiment focuses on finding the refractive index of the bi-convex lens.…

• 1124 Words
• 4 Pages
Decent Essays
• Decent Essays

After this, I converted the left-side to square form plus a bit of simplifying on the right: = From this point, I began to square root both sides and remembered to put the sign on the right: x. Once I did that, I solved for x and simplified as necessary: x= By evaluating the answer, it finally resulted in the Quadratic Formula: Problem 2: 2x?-x+2=0 Rewriting in vertex form: Before I rewrote the quadratic equation of 2x?-x+2=0 in vertex form, I had to understand that the vertex form of a quadratic function is f(x)=a(x-h)?+k where…

• 780 Words
• 4 Pages
Decent Essays
• Decent Essays

The following formula represents the quadratic formula:x=(-b±√(b^2-4ac))/2a After plugging each number to their corresponding term, it must first look like the following x=(-(-1)±√(〖(-1)〗^2-4(2)(2)))/(2(2))Next “-1” is multiplied by a negative which equals to a positive “1”. Moreover, the discriminant must be simplified and equal to √(1-16) which equals to √(-15). In math, a square root must never be negative, so an “i” which stands for imaginary number will replace the negative sign and cancel out the square root. Now the quadratic formula looks like the following: x=(1±√(-15))/(2(2)). Then, the denominator is simplified by multiplying “2” times “2” which equals to “4”.…

• 1468 Words
• 6 Pages
Decent Essays
• Decent Essays

When the credit terms don’t appear on the invoicing sheet I will have to email Tammy at Tip Top to find out from her before giving the invoicing sheet to Neela for review. The reply email from Tammy will have to be attached to the back after invoicing sheet. I will need to update the contact sheet for Tip Top with new email addresses when customer provides me with new email address or when Tammy sends me new customers to set up. The invoice will need to be duplicated from existing invoice or a new one will be created from the beginning. All the invoices together with the invoicing sheets will be put in the for review folder that is labeled Tip…

• 1166 Words
• 5 Pages
Decent Essays
• Decent Essays

THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point.…

• 2362 Words
• 10 Pages
Decent Essays
• Decent Essays

By figuring out the color position, we looked at the fraction of the red and greens light orange has; .75R and .2G. In order to find out the fraction of blue, we used the equation 1 = r+ g +b because the fractions of red, green and blue equal to one (Gilbert 103). We substituted in r and g and got b by itself; in order to get b by itself, we subtracted r and g from both sides resulting in b = 1 - r -g. The fraction of blue is .05. Next we calculated the…

• 799 Words
• 4 Pages
Decent Essays
• Decent Essays

I encouraged the students to explain their mathematical reasoning. Through ED 360, I learned the importance of going beyond the typical asked questions to students during math. In class we discussed we need to ask questions that encourage the students to use their higher-level thinking. For example, the following questions will engage students in higher level thinking and mathematical reasoning: “Is there another way to get this answer?” and/or “Can you explain how you got your answer?”. This strategy is from the National Council of Teachers for Mathematics, “Teaching and Learning Principles from PtA”, which entails asking essential questions that are to be a catalyst for deeper levels of thinking (NCTM, 2014).…

• 1319 Words
• 6 Pages
Decent Essays
• Decent Essays

Even the National council of mathematics have decided to make it compulsory to teach different ways to use pattern in class, so that the kids have better understanding of the topic. This is the minimal requirements put up by the council because it helps people with reasoning and quicker problem solving. The Pascal’s triangle in the mathematical word is a simple representation of numbers in an array and is a binomial coefficient. The Pascal’s theorem is said to be discovered by Bailey Pascal. Whereas historians…

• 1202 Words
• 5 Pages
Decent Essays
• Decent Essays

It is named in honor of Benjamin Bevan. The Bevan point is the reflection of Incenter in the Circumcenter and it is also the reflection of orthocenter in the Spieker center. The Bevan point(V) is the midpoint of line segment joining the Nagel point and de-Longchamps point.The Bevan point(V) is a triangle center and it is listed as the point X(40) in Clark Kimberling’s Encyclopedia of Triangle Centers. Lemma – 1 If is the area of pedal’s triangle with respect to the any arbitrary point P, and if is the area of reference triangle then prove that Among all the pedal’s triangles, the pedal triangle with respect to some point P whose area is one fourth of the area of the reference triangle, has maximum area. That is .…

• 785 Words
• 4 Pages
Decent Essays