Solving Trigonometric Equations Unit 5D Day 1

Do Now  Fill in the chart. This must go in your notes! θsinθcosθtanθ 0º 30º 45º 60º 90º

Trigonometric Equations  A trigonometric equation is an equation that contains a trigonometric function, such as sine and cosine.  Ex.: cosθ = ½  Ex.: 2sinθ – 1 = 0

Signs of Trigonometric Functions  Quadrant I  Sine is _________  Cosine is _________  Tangent is ________  Cosecant is ________  Secant is ________  Cotangent is ________

Signs of Trigonometric Functions  Quadrant II  Sine is _________  Cosine is _________  Tangent is ________

Signs of Trigonometric Functions  Quadrant III  Sine is _________  Cosine is _________  Tangent is ________

Signs of Trigonometric Functions  Quadrant IV  Sine is _________  Cosine is _________  Tangent is ________

Signs of Trigonometric Functions  Mnemonics for Positive:  All Students To Class  All Stores Take Cash  Awfully Stupid Trig. Class

Solving Trig. Equations  Ex. 1: Find all the values of θ that make cosθ= ½.  The sign of cosθ is ___________ so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.  Technically, there are infinitely many solutions!

Solving Trig. Equations  Ex. 2: Find all the values of θ that make sinθ= - √3 / 2 for 0 ≤ θ < 360º.  The sign of sinθ is ___________ so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.

Reciprocals  For cosecant or secant, we have to start by _________________________ of both sides to get sine or cosine.

Solving Trig. Equations  Ex. 4: Find all the values of θ that make secθ= 2√3 / 3 for 0 ≤ θ < 360º.  The sign of secθ is ___________, and secθ is the reciprocal of ___________, so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.

Solving Trig. Equations  Ex. 4: Find all the values of θ that make cscθ= -2 for 0 ≤ θ < 360º.  The sign of cscθ is ___________, and cscθ is the reciprocal of ___________, so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.

Reference Angles  For tangent and cotangent, we will refer to the chart (from the do now) and use reference angles.

Solving Trig. Equations  Ex. 5: Find all the values of θ that make tanθ= 1 for 0 ≤ θ < 360º.  The sign of tanθ is ___________, so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.

Solving Trig. Equations  Ex. 6: Find all the values of θ that make tanθ= -√3 for 0 ≤ θ < 360º.  The sign of tanθ is ___________, so our answer could be in quadrant ______ or _______.  The two solutions on our unit circle are _______ and ________.