Students acquisition trigonometry process are familiar with the Pythagorean theorem and also the simple trigonometric properties connected with the right triangle. Learning the various trigonometric identities can aid students solve and also simplify many trigonometric problems. Identities or trigonometric equations v cosine and also secant are commonly easy come manipulate if you understand their relationship. By using the Pythagorean theorem and also knowing just how to uncover cosine, sine and also tangent in a appropriate triangle, you have the right to derive or calculation secant.

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Draw a right triangle with 3 points A, B and C. Allow the suggest labeled C be the appropriate angle and draw one horizontal heat to the appropriate of C to point A. Attract a vertical line from suggest C come the allude B and also draw a heat between allude A and allude B. Label the political parties respectively a, b and also c, where side c is the hypotenuse, next b is opposite angle B, and side a is opposite edge A.


Know the the Pythagorean theorem is a² +b²= c² where sine the an angle is the opposite side split by the hypotenuse (opposite/hypotenuse), while the cosine of the edge is the surrounding side separated by the hypotenuse (adjacent/hypotenuse). The tangent of an angle is the opposite side split by the nearby side (opposite /adjacent).


Understand the to calculation secant you require only uncover the cosine of one angle and the relationship that exists in between them. So friend can discover the cosine of angles A and also B native the diagram by utilizing the definitions given in step 2. These are cos A= b/c and cos B=a/c.


Calculate secant by finding the reciprocal of the cosine of one angle. Because that the cos A and also cos B in action 3, the reciprocals are 1/cos A and also 1/cos B. So sec A = 1/cos A and also sec B= 1/cos B.


Express secant in regards to the political parties of the best triangle by substituting cos A =b/c into the secant equation for A in action 4. You uncover that secA= 1/ (b/c) =c/b. Similarly, you view that secB=c/a.


Practice finding secant by solving this problem. You have a appropriate triangle comparable to the one in the diagram where a=3, b=4, c=5. Find the secant of angle A and also B. First find cos A and cos B. From action 3, you have cos A= b/c=4/5 and also for cos B=a/c=3/5. From step 4, you see that sec A= (1/cos A) =1/ (4/5) = 5/4 and also sec B= (1/cosB) =1/ (3/5) =5/3.

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Find secθ when "θ" is offered in degrees by using a calculator. To find sec60, usage the formula sec A = 1/cos A and also substitute θ =60 degrees for A to gain sec60= 1/cos60. ~ above the calculator, uncover cos 60 by pushing the "cos" function key and input 60 to gain .5 and calculate the reciprocal 1/.5 =2 by pushing the station function key "x -1 " and also entering .5. So for an angle that is 60 degrees, sec60 = 2.