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Angles and Degree Measure We will begin by measuring angles in degrees. Recall that one degree is equal to 1/360 of a complete revolution. You can generate any angle by using a rotation that moves one of the rays forming the angle, called the initial side, onto the other ray, called the terminal side. Angles and Degree Measure An angle is in standard position when its initial side coincides with the positive x-axis. Angles can be classified by where their terminal side lands. An angle is considered a quadrantal angle when its terminal side lies on a coordinate axis. Angles and Degree Measure Sketch each angle on your “whiteboard”. Then estimate the measure of each of the following angles: Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 170 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 170 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 190 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 210 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 300 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 100 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 95 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 450 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 400 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 265 Angles and Degree Measure Sketch the angle with the given measure on the coordinate axes. 530 Angles and Degree Measure Two angles in standard position are coterminal if their terminal sides coincide. Ex) Find two coterminal angles for the angle shown. Angles and Degree Measure To measure angles more precisely, consider how they can be broken down: Angles and Degree Measure Ex) Convert 14 36' 54" to decimal degrees. Ex) Convert 72.568 to degrees, minutes, and seconds Learning Log Summary LT 1 – I can use degree measure to sketch an angle in standard position and convert between different forms of degree measure. Angles in standard position… Positive vs negative angles are… Coterminal angles are… Trigonometric Functions To define the trigonometric functions of an angle θ, place θ in standard position. Then choose any point P (x,y) on the terminal side of θ and let r be the distance OP. Trigonometric Functions An acute angle θ is in standard position and its terminal side passes through (6 , 8). Find sinθ, cosθ and tanθ. Trigonometric Functions An acute angle θ is in standard position and its terminal side passes through (3 , 5). Find sinθ, cosθ and tanθ. Trigonometric Functions Find sinθ and tanθ if θ is an acute angle and if cosθ=2/7. Trigonometric Functions Find sinθ and cosθ if θ is an acute angle and if tanθ=8/3. Trigonometric Functions If cosθ=3/4, find the value of cos(- θ). Trigonometric Functions If sinθ=1/2, find the value of sin(180- θ). Trigonometric Functions Trigonometric Functions Trigonometric Functions Learning Log Summary LT 2 – I can define the sin, cos, and tan of an angle using a point on the terminal side of the angle. Sin, Cos, Tan of an angle are… To find the missing side of a right triangle… If given the value of a trig function of an angle… Closure Homework Problem Set #1 (Copy of Book Pages) Warm-Up Find the measure of the missing side/angle in each diagram. Round answers to the nearest hundredth. Law of Cosines Law of Cosines In a general triangle ABC: a b c 2bc cos A 2 2 2 b a c 2ac cos B 2 2 2 c a b 2ab cos C 2 2 2 To use the Law of Cosines… Law of Cosines Ex 1) Find the length of side a to the nearest hundredth: Law of Cosines Ex 2) Find the length of side c to the nearest hundredth: Law of Cosines Ex 3) Find the measure of each angle of triangle ABC in the diagram below. Law of Cosines Ex 4) A navigator plots the course a plane is currently traveling. The plane is 300 miles from its destination. If it continues on its current course it will travel 325 miles and end up 125 miles due south of its destination. To the nearest degree, how many degrees is the plane off course? Learning Log Summary LT 8 – I can apply the law of cosines to find missing sides and angles of any triangle. The Law of Cosines is useful if… To find a missing side/angle using the Law of Cosines… Closure Homework pg. 582 ~ 1-11 (Odd) pg. 583 ~ 1-7 (odd) Law of Cosines – Partner Problems! Law of Cosines – Partner Problems! Law of Cosines – Partner Problems! Law of Cosines – Partner Problems! Law of Cosines – Partner Problems! Law of Cosines – Partner Problems!