Algebraic Statement

Given the right triangle below, find cos?, sin?, tan?, sec?, csc?, and cot?. Do not estimate: Find exact answers. Show all of your work and explain the steps as necessary.

Trigonometric functions Geometry

I. The connection between the lengths of the sides of this right-angle triangle and theta (?) is clarified through the accompanying trigonometric functions including (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot) functions.

II. [bookmark: _Hlk533622677]a. The Pythagorean theorem formula can be used for inserting the length of the remaining side of the right-angle triangle shown on top of the page which is the adjacent side. Given that picture of the right triangle from our template we have been provided for this assignment with the length of the hypotenuse “7” and opposite side “4”, we can calculate the length of remaining adjacent side using the Pythagorean theorem formula. The “a” represents the length of the adjacent side. Here is how u find the missing side the adjacent side.

· a2 = 33

b. Here are the six trigonometry functions showing the connection between theta and the three sides of the first right-triangle picture up top.

Trigonometry Functions and relationship to Theta:

1. sine(theta) = opposite / hypotenuse

2. cosecant(theta) = hypotenuse / opposite

3. cosine(theta) = adjacent / hypotenuse

4. secant(theta) = hypotenuse / adjacent

5. tangent(theta) = opposite / adjacent

6. cotangent(theta) = adjacent / opposite

Along these lines, the connection/answers between theta and the sides of the right-angle triangle appeared above is as shown on the next page.

Sine function: sin ? = opposite/hypotenuse sin ? =

Cosine function: cos ? = adjacent/hypotenuse cos ? =

Tangent function: tan ? = opposite/adjacent tan ? =

Cosecant function: csc ? = hypotenuse/opposite csc ? =

Secant function: sec ? = hypotenuse/adjacent sec ? =

Cotangent function: cot ? = adjacent/opposite cot ? =

A calculator can be used to find the value of ? in degrees. In this case to find the value of ? we know the following will be equal to sin-1 (= cos-1() = tan-1(= csc-1( ) = sec-1() = cot-1() = 34.850.

Knowing that the above triangle is absolutely a right-angle triangle, we can easily determine the value of the remaining angle as shown on the example beneath us.

[1800 – (900 + 34.850)]

= [1800 – 124.850]

= 55.150

Conclusion

In the algebra statement, I stated above, the numerator and denominator of the first section are the same; therefore, we can simply evaluate this to get what is shown in the example beneath.

Next step is that given that the statement has two components; the x and y components, we can use simple algebra to factor out these parts for easy computation. Once completing factoring out these two components, we get this statement.

Second, we can use the sum of difference formula to simplify the numerator of the equation statement since it would be no possibility to solve it without simplifying the numerator in this equation. There are four possibilities Here they are. As we know the numerator for this problem statement for this assignment is , therefore, in the above sum of difference formulas the equivalent to, which is equivalent to the simplified form.

In addition, since we can’t solve the identity with the numerator as it is without simplifying it first, it is right to simplify it based on the sum of difference formulas above so it can effectively solve the identity. Using the sum of difference formula to solve the identity, we get the equation shown below:

Last but not least we can use the quotient identities to work out the final outcome to this. There are two quotient identities that we know to are the knowledge that is shown beneath. Knowing that the second term of statement has the form of , we can simply use the quotient identities to solve this. Using the quotient identities, we will obtain the following statement:

In conclusion, we have clearly added the trigonometric function to verify the identity:

REFERENCES:

ADendane@uaeu.ac.ae. (n.d.). Free Mathematics Tutorials. Retrieved from http://www.analyzemath.com/trigonometry/properties.html

How to Calculate Values for the Six Trigonometric Functions. (n.d.). Retrieved from https://www.dummies.com/education/math/calculus/how-to-calculate-values-for-the-six-trigonometric-functions/

(n.d.). Retrieved from https://study.com/academy/lesson/trigonometric-functions-definition-examples-quiz.html

(n.d.). Retrieved from https://study.com/academy/lesson/trigonometric-functions-definition-examples-quiz.html

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