- "Review of Trigonometric Functions - Triangle Solutions & Sin Value Calculation
- Trigonometry plays a crucial role in solving triangles by finding unknown measurements of their parts. This review covers the concept of solving a triangle given three known measurements. The lecture also explains how a circle with a radius of 1 can determine the value of sin(x) at a certain degree. Explore this comprehensive review of trigonometric functions presented by Mr. Brwa Ahmed from Tishk International University.
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Mathematics Lecture 2 / Review of Trig. Functions Spring Semester 2019 Instructor Instructor A. S. Brwa A. S. Brwa MSc . Structural Engineering MSc . Structural Engineering brwa.ahmed@ishik.edu.iq brwa.ahmed@ishik.edu.iq Faculty of Engineering Faculty of Engineering Tishk Tishk InternationalUniversity InternationalUniversity
Tishk International University Review of Trigonometric Functions Trigonometry can be used to figure out unknown measurements of parts of triangles. Figuring out the unknown measurements of ALL of the parts of a triangle is called Solving a Triangle . Usually, you can solve a triangle if you know the measures of three parts of the triangle. 2 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
Tishk International University Review of Trigonometric Functions We take a circle with center at the origin, and with radius 1. We then draw a line from the origin, at x degrees from the horizontal axis, until it meets the circle, so that the line has length 1. We then look at the vertical axis coordinate of the point where the line and the circle meet, to find the value of sin x. 3 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
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Tishk International University Review of Trigonometric Functions Opposite Adjacent ????? =???????? ???????? ???? =???? 10 ???? Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
Tishk International University Review of Trigonometric Functions The sixtrigonometric functions of a right triangle, with an acute angle ?,are defined by ratios of two sides of the triangle. hyp opp The sides of the right triangle are: the side opposite the acute angle , adj the side adjacent to the acute angle , and the hypotenuse of the right triangle. 11 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
Tishk International University Review of Trigonometric Functions hyp The six trigonometric functions are as follows opp adj sin? =??? ??? ??? tan? =??? ??? cos? = ??? ???? = 1 1 1 ????sec? = ????cot? = ???? ???? =??? ???sec? =??? ??? ??? 12 ???cot? = Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
Tishk International University Review of Trigonometric Functions Example-1: Refer to the triangle shown below, find the six trigonometric function values of a) ? b) ? Ans. (a) ????=13 1 sin? =??? ??=12 csc? = 12 13 ????=13 1 ??? ??= 5 13 sec? = 5 cos? = 1 5 12 tan? =??? ???=12 ???? = ????= 5 13 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
Tishk International University Review of Trigonometric Functions Example-1: Refer to the triangle shown below, find the six trigonometric function values of a) ? b) ? Ans. (b) ????=13 1 sin ? =??? 5 13 csc? = 5 ??= ??? ??=12 ????=13 1 13 cos? = sec? = 12 tan? =??? 5 12 ????=12 1 14 ???= co?? = 5 Mr. Brwa Ahmed: Faculty of Engineering Math II Lecture 2 Review of Trigonometric Functions
THANKS I HOPE YOU HAVE ENJOYED MY CLASS
