Students acquisition trigonometry process are acquainted with the Pythagorean theorem and also the basic trigonometric properties connected with the ideal triangle. Knowing the various trigonometric identities can help students solve and also simplify plenty of trigonometric problems. Identities or trigonometric equations with cosine and secant are generally easy come manipulate if you recognize their relationship. By utilizing the Pythagorean theorem and also knowing just how to discover cosine, sine and also tangent in a right triangle, you can derive or calculation secant.

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Draw a best triangle with 3 points A, B and C. Allow the allude labeled C it is in the ideal angle and also draw one horizontal line to the right of C to suggest A. Draw a vertical line from allude C to the suggest B and likewise draw a line between suggest A and suggest B. Label the political parties respectively a, b and also c, where side c is the hypotenuse, side b is opposite edge B, and also side a is opposite edge A.

Know that the Pythagorean theorem is a² +b²= c² wherein sine the an angle is the opposite side divided by the hypotenuse (opposite/hypotenuse), if the cosine the the edge is the nearby side separated by the hypotenuse (adjacent/hypotenuse). The tangent of an angle is opposing side separated by the nearby side (opposite /adjacent).

Understand that to calculation secant you need only discover the cosine of an angle and also the relationship that exists in between them. So friend can find the cosine of angle A and also B indigenous the diagram by making use of the definitions given in step 2. These room cos A= b/c and also cos B=a/c.

Calculate secant by finding the mutual of the cosine of an angle. For the cos A and cos B in step 3, the reciprocals space 1/cos A and also 1/cos B. Therefore sec A = 1/cos A and sec B= 1/cos B.

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

Practice detect secant by resolving this problem. You have actually a ideal triangle comparable to the one in the diagram wherein a=3, b=4, c=5. Find the secant of angle A and also B. An initial find cos A and also cos B. From step 3, you have cos A= b/c=4/5 and for cos B=a/c=3/5. From action 4, you check out 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 given in degrees by making use of a calculator. To find sec60, usage the formula sec A = 1/cos A and substitute θ =60 degrees for A to gain sec60= 1/cos60. ~ above the calculator, uncover cos 60 by pressing the "cos" function key and input 60 to obtain .5 and calculate the reciprocal 1/.5 =2 by pressing the train station function vital "x -1 " and also entering .5. So because that an angle that is 60 degrees, sec60 = 2.