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## PLANE TRIGONOMETRY

by: Maverick Koelpin

17

0

6

# PLANE TRIGONOMETRY MATH 1022

Maverick Koelpin
LSU
GPA 3.77

G. Fitch

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COURSE
PROF.
G. Fitch
TYPE
Class Notes
PAGES
6
WORDS
KARMA
25 ?

## Popular in Mathematics (M)

This 6 page Class Notes was uploaded by Maverick Koelpin on Tuesday October 13, 2015. The Class Notes belongs to MATH 1022 at Louisiana State University taught by G. Fitch in Fall. Since its upload, it has received 17 views. For similar materials see /class/222622/math-1022-louisiana-state-university in Mathematics (M) at Louisiana State University.

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Date Created: 10/13/15
SECTION 74 TRIGONOMETRIC FUNCTIONS OF GENERAL ANGLES Study Text Examples 18 FIND THE EXACT VALUES OF THE TRIGONOMETRIC FUNCTIONS FOR GENERAL ANGLES De nition Let 6 be an angle in standard position andlet Pabbe a point on the terminal side If r a2 12 is the distance from the origin to the point Pab then sing 005639g tan6 a 0 r r a csc 9 b 0 sec6 a 0 cot6gb 0 b a b Example 1 Find the EXACT value of the siX trigonometric functions of a positive angle Oif 1 2 is a point on its terminal side sin9 cos6 tan6 csc6 sec6 cot9 FIND THE EXACT VALUES OF THE TRIGONOMETRIC FUNCTIONS OF QUADRANTAL ANGLES de ned de ned de ned de ned DETERMINE THE SIGNS OF THE TRIGONOMETRIC FUNCTIONS OF AN ANGLE IN A GIVEN QUADRANT 6 USE REFERENCE ANGLE TO FIND THE EXACT VALUE OF A TRIGONOMETRIC FUNCTION De nition Let 6 be an angle in standard position The reference angle or associated with 6 is the acute angle formed by the terminal side of 6 and the X aXis FINDING THE VALUES OF THE TRIGONOMETRIC FUNCTIONS OF A GENERAL ANGLE Ifthe angle 6 is a quadrantal angle draw the angle pick a point on its terminal side and apply the de nition of the trigonometric functions Ifthe angle 6 lies in a quadrant 1 Find the reference angle a of 6 2 Find the value ofthe trigonometric function at a 3 Adjust the sign or according to the sign of the trigonometric function in the quadrant where 6 lies Example 2 Find the exact value for 57139 57139 a srn b cos 3 l 4 0 tan 7 d 030 71 6 3 117239 157139 e cot sec 6 r 4 SECTION 104 VECTORS Study Text Examples 17 De nition Quantities such as length mass area temperature and energy are determined by their magnitude and are called scalar De nition Quantities that require both magnitude and direction are vectors such as displacement velocity acceleration and force Geometric Vectors De nition A vector in the plane is a line segment with an assigned direction PQ This is vectorPQ and point P is the initial point and point Q is the terminal point De nition Egual vectors have the same magnitude and direction gt De nition The sum v w of two vectors is positioned so that the terminal point of v coincides with the initial point of w Adding Vectors Properties vwwv uvwuvw vv0 v00vv v wvw Multiplying Vectors by Numbers lforis a scalar and vis a vector orv ifor gt 1 stretches and if0 lt or lt 1 shrinks If orgt 0 vector goes in same direction and ifor lt 0 vector goes in opposite direction To go from the initial point ofv to the terminal point we move a units right and b units up v lt a b gt where a is the horizontal component and b is the vertical component Magnitudes of Vectors The length or magnitude of the vector v is Properties If vis a vector and if or is a scalar then a HVH 2 0 b HVH 0ifand only ifv 0 c H VHHVH d How aH vH A vector u for which US called a unit vector Algebraic Vectors De nition An algebraic vector vis represented as v ltabgt where a and b are real numbersscalars called the components of the vector v If v ltabgt is an algebraic vector whose initial pointis at the origin then vis called a position vector Theorem If vis represented in the plane with initial pointP X1 y1 and terminal pointQ X2 y2 then v ltX2 X1y2 y1 gt An alternative representation of a vector Leti denote the unit vector lt10gt and j denote the unit vector lt01gt Then any vector v ltabgt can be written usingi andj v ltabgt alt10gt blt01gt ai bj Properties Let ua1ib1j lta1b1gtandva2ib2j lta2 b2gt then UVa132ib1 b2jlta182b1 b2gt U39Va13932ib1 b2jlta132b1 b2gt duora1iorb1jltora1orb1gt Magnitude orlength ofv lt a b gt is M laz b2 Example 1 Find the position vector of v PQ if P 1 2 and Q 3 5 Example 2 lfu lt 2 7gt andv lt31gt nd3u 4v V Theorem For any nonzero vector v the vector u N Is a unIt vector that has V the same direction as v Example 3 Find a unit vector in the same direction as v 5i 12j In many applications a vector can be described in terms of its magnitude and direction instead of its components To express v in terms of and a V HvHcosaisin og39 where or is the angle between vand the positive xaxis Example 4 A child pulls a wagon with a force of 40 pounds The handle of the wagon makes an angle of 30 with the ground Express the force vectorF in terms ofi andj

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