Precalculus – HollyerChapter 4 – Lecture BAnnouncementsQuiz 6 and Quiz 7 BOTH go down togetherHomework 16 (today’s lecture) closes 1Chapter 4, Section 3Note that the values for the trigonometric functions can be either negative, positive, zero or undefined. Put on the quadrantal angles in radian measure (cosine, sine) Unit Circle Trig!Note now how I specify quadrants in radian measure:Q1 0 <  < 2p Q3 < 90°Q2 Q42Quadrant Practice:Suppose 322 2p p<a <p <b< pfill in either < or > in the following statement:cos sin Calculation Practice:Suppose you have a point P on the unit circle and you don’t know  but you do know onepoint coordinate:for example x =  4/5 . This puts P in Q2 or Q3 because it’s cosine is negative. Suppose further that I tell you :2p<q<p. Which quadrant is this?What is tan()? 3Popper 07, Question 14A reference angle for a given angle is a Quadrant 1 angle of the same measure as the given angle up or down from the x axis. The given angle has the same trigonometric function values in absolute value as the reference angle. The standard ones are 30°, 45°, and 60°, but any Quadrant 1 angle can be a reference angle.Co-terminal angles are angles of different measure that share the same terminal ray.(cos , sin ) = (+, +)Our initial ray is always along the positive x axis. Our terminal ray can move to any quadrant.Note the 3 other angles referenced by  . They have the same trigonometric function values within a +/−.Show 2 co-terminal angles.Where is 76p-? What is the Quadrant 1 reference angle for this rotation?What positive angle is it co-terminal with? What would the cos be − first with it’s reference angle value, then the number itself?What about 403°? What is the Quadrant 1 reference angle for this rotation? Note: not only is it a reference angle, the given angle is co-terminal with its reference angle!5Popper 07, Question 26In Quadrant 1 the following are very important:Know this by heart! OYOangle in deg 0 30 45 60 90angle in radsinecosinetangentOn the boundaries of the quadrants are the Quadrantal Anglesfor example:32pq= is a quadrantal angle!What is 3sin( )2p?What is tan (360)? tan (720°)?Co-terminal! What is sec()?7Popper 07, Question 38Looking at angles that reference 6sin 6 = cos 6 = Write down all the angles that reference 6 in one rotation:List 3 angles co-terminal with 6. Make sure one is a negative rotationLocate and evaluate:Quiz 7, all questionssin (210°) 611cot =7sin( )6p- =9Popper 07, Question 410And those referencing 4: sin 4 = cos 4 =Write down all the angles that reference 4 in onerotation:List one negative and 2 positive angles co-terminal with 315°:Quiz 7 all questionsLocate and evaluate:43cos = 45sec = sin( 45 )- �=11Popper 07, Question 512And those referencing 3: sin 3 = cos 3 =Write down all the angles that reference 3 in onerotation :Write down one negative and 2 positive angles that are co-terminal with 23p:Quiz 7, all questionsLocate and evaluate:32tan=csc(420 )� = )32cos(=13Popper 07, Question 614Find 3 angle measures (1 negative and 2 positive) co-terminal with58pName the reference angle and find the valuetan(135 )�11sin6pcos2pIf sin t = 3and t4 2p< <p, compute cot t.15Popper 07, Question 716Example:If cos x = 3/5 and 3x2pp< <, compute csc x.17Popper 07, Question 8 Quiz 7 problems18Popper 07, Question 919Popper 07, Question