WarmUp Exercises Find the sine cosine and tangent

Warm-Up Exercises Find the sine, cosine, and tangent of the angle. 1. 90° ANSWER 1, 0, undefined 2. 360° ANSWER 0, 1, 0

Warm-Up Exercises Determine whether the trigonometric function of the angle is positive or negative. 3. sin 250° ANSWER negative 4. cos 330° ANSWER positive 5. sin 370° ANSWER positive

Example 1 Graph a Sine Function Graph y = sin 180 x. Find the characteristics of the graph using a = 1 and b = 180. There is one intercept at (0°, 0 ) and the period 360° is = 2°. 180 Find two other intercepts. 180° , 0 = (1°, 0 ) b 180 360° , 0 = , 1 = ( 2°, 0 ) b 180

Example 1 Graph a Sine Function Find the maximum and minimum. 90° , a = , 1 = (0. 5°, 1 ) b 180 270° , –a = , – 1 = ( 1. 5°, – 1 ) b 180

Example 2 Graph a Cosine Function Graph y = 2 cos x. Find the characteristics using a = 2 and b = 1. Because b = 1, you can see that two intercepts are at ( 90°, 0 ) and ( 270°, 0 ), and the period is 360°. The maximums are at ( 0°, a ) = ( 0°, 2 ) 360° and , a = ( 360°, 2 ). b The minimum is at 180° , – a = ( 180°, – 2 ). b

Example 3 Graph a Tangent Function Graph y = tan 2 x. SOLUTION Use a = 1 and b = 2 to find the key points on the interval 90° – , or – 45° < x < 45°. x < < 2 2 STEP 1 Plot the x-intercept at ( 0°, 0 ). STEP 2 Draw the vertical asmptotes. x = – 90° – = = – 45° b 2

Example 3 Graph a Tangent Function 90° x = = = 45° 2 b STEP 3 Plot the halfway points. – 45° , – a = – 45° , – 1 = ( – 22. 5°, – 1 ) b 2 45° , a = , 1 = ( 22. 5°, 1) b 2 Notice that the period of y = tan 2 x is So, one period is shown. 180° = = 90°. b 2

Checkpoint Graphing Sine, Cosine, and Tangent Functions Graph the function. 1. y = 2 sin x ANSWER

Checkpoint Graphing Sine, Cosine, and Tangent Functions Graph the function. 2. y = cos 360 x ANSWER

Checkpoint Graphing Sine, Cosine, and Tangent Functions Graph the function. 3. y = 3 tan x ANSWER