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# Review Sheet for MATH 1330 at UH

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This 5 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 16 views.

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Date Created: 02/06/15

Example 2 Find x 5J5 Ll Example 3 gtlt m Example 4 Example 5 I Example 6 Find x I Example 7 Find x x Example 8 Find x 30 10 Example 9 Find x The Six Trigonometric Functions of an Angle Suppose we are given a right triangle ABC where AC 90 We de ne the trigonometric functions of either of the acute angles of the triangle as follows length of the side opposite 0 sin 19 length of hypoteneuse cos 0 length of the Side adjacent t0 19 length of hypoteneuse tang length of the side 0pp0s1te 19 length of the Side adjacent t0 0 cs length of the hypoteneuse length of the side opposite 19 sec 0 length of the hypoteneuse length of the side adjacent t0 t9 cote length of the Side adjacent t0 19 length of side opposite t0 t9 Example 10 Given AABC a Find a b Find the six trigonometric functions of angle A c Find the six trigonometric functions of angle B Example 11 Find the six trigonometric functions of a and 15 Example 12 Suppose that ADEF is a right triangle andD is an acute angle If sinD g find the other five trig functions of angle D Example 13 Suppose that 6 an acute angle in a right triangle and csct9 Find the other five trig functions of angle 0 Example 14 Suppose that 6 an acute angle in a right triangle and tan 0 g Find the other five trig functions of angle 0 Example 15 Find the six trigonometric functions of angles measuring 30 degrees 45 degrees and 60 degrees Math 1330 Section 41 Special Triangles and Trigonometric Functions In this section we ll work with some special triangles before moving on to de ning the six trigonometric functions Two special triangles are 30 60 90 triangles and 45 45 90 triangles With little additional information you should be able to nd the lengths of all sides of one of these special triangles First we ll review some conventions when working with triangles We label angles with capital letters and sides with lower case letters We ll use the same letter to refer to an angle and the side opposite it although the angle will be a capital letter and the side will be lower case In this section we will work with right triangles Right triangles have one angle which measures 90 degrees and two other angles whose sum is 90 degrees The side opposite the right angle is called the hypoteneuse and the other two sides are called the legs of the triangle A labeled right triangle is shown below b C In a 30 60 90 triangle the lengths ofthe sides are proportional Ifthe shorter leg the side opposite the 30 degree angle has length a then the longer leg has length xga and the hypoteneuse has length 2a An easy way to remember this is to write the lengths in ratio form as a J36 2a So if you know or can nd a you can nd the lengths of all three sides In a 45 45 90 triangle the two legs ofthe triangle are equal in length This triangle is also called an isosceles right triangle Ifthe legs each measure a then the hypoteneuse has length xEa The ratio to remember for these triangles is a a xEa Again if you know a you can nd the lengths of all three sides Example 1 Find x

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