6.4 - Trig Ratios in the Coordinate Plane Page 452 24) 25) 26) 27) 28) 29) 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

Trig Ratios in the Coordinate Plane Section 6.4 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Review Determine the Trigonometric Functions for Ѳ 5 4 3 SIN ө= COS ө = TAN ө = CSC ө = SEC ө = COT ө= 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

Equation in Standard Form For ө be an angle in standard position with any point (x, y) SIN ө = y/r COS ө = x/r TAN ө = y/x CSC ө = r/y SEC ө = r/x COT ө = x/y B. To establish the radius, the equation is 𝒓= 𝒙 𝟐 + 𝒚 𝟐 C. Think of “ASTC: All Students Take Calculus” A: All points are always positive in Quadrant I S: Sine points are positive in Quadrant II T: Tan points are positive in Quadrant III C: Cosine points are positive in Quadrant IV 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

Equation in Standard Form For ө be an angle in standard position with any point (x, y): S A When ALL trig functions are positive When SIN is positive Quadrant II (– , +) Quadrant I (+, +) T C When TAN is positive When COS is positive Quadrant III (–, –) Quadrant IV (+, –) “All Students Take Calculus” 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

Steps in Evaluating Functions given a Point Draw a picture from a coordinate plane Identify and plot the point onto the coordinate plane Determine the missing side using the radius equation Use Trigonometric Functions to solve 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Example 1 Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 4 3 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Example 1 Let (3, 4) be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. 3 4 5 SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Example 2 Let 𝟏𝟎 𝟏𝟎 ,− 𝟑 𝟏𝟎 𝟏𝟎 be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Your Turn Let 𝟏,−𝟏 be a point on the terminal side of ө. Determine the value of the six trigonometric functions for ө. SIN ө = COS ө = TAN ө = CSC ө = SEC ө = COT ө = 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

Finding the Exact Value Without a Calculator Make sure the calculator is set in RADIAN mode Apply all three trig functions Determine which quadrant it belongs to identify the quadrant of the terminal side 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Example 3 Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for − 𝟏𝟏 𝟓 𝝅 Quadrant I (+, +) Quadrant II (– , +) Quadrant IV (+, –) Quadrant III (–, –) 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Example 4 Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for 𝟖 𝑹𝒂𝒅𝒊𝒂𝒏 Quadrant I (+, +) Quadrant II (– , +) Quadrant IV (+, –) Quadrant III (–, –) 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Your Turn Use a calculator, in radian mode, to find sin, cos, and tan of the quadrant of the terminal side for −𝟐𝟑𝝅 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane

6.4 - Trig Ratios in the Coordinate Plane Assignment Pg 452 1-9 odd (List all 6 Trig Functions) 15-23 odd 5/6/2019 11:30 PM 6.4 - Trig Ratios in the Coordinate Plane