# RGCT_Task_3_Revision - Ө 2 This identity is formulated...

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2 RGCT Task 3 Trigonometric Equations and Identities The Pythagorean identities can be defined once we understand the Pythagorean theorem. The Pythagorean theorem states that in a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides (Pierce, 2010). In essence this can be written as the equation a 2 + b 2 = c 2 . With the Pythagorean identity sin 2 + cos Ө 2 = 1, remember that sin is equivalent to the Ө Ө y-coordinate point and cos is equivalent to the x-coordinate point on the unit circle. When we Ө implement the right triangle from these points, and utilize the Pythagorean theorem we can understand the answer sin 2 + cos Ө 2 = 1. Ө sin 2 + cos Ө 2 = Ө + The next identity is tan 2 + 1 = sec

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Unformatted text preview: Ө 2 . This identity is formulated when the original Ө identity is divided on both sides by cos 2 . Ө The final identity is cot 2 + 1 = csc Ө 2 . This identity is created when the original identity Ө is divided on both sides by sin 2 . Ө Proof The denominator must be the same when working subtraction with fractions.- ( Next utilize the distributive property Combine like terms Simplify 3 Running head: RGCT TASK 3 We utilize the Pythagorean identity to modify the top of the fraction. Simplify. Zero divided by any number is still zero. We have made the left side of the equation equal the right side of the equation. 4 References Pierce, R. (2010, April) "Pythagoras Theorem" Math Is Fun. Ed. Rod Pierce. Retrieved August 10, 2010 from http://www.mathsisfun.com/pythagoras.html...
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