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Example 1 Draw Angles in Standard Position Draw an angle with the given measure in standard position. 215° a. 410° b. 60° c. – SOLUTION a. Because 215° is 35° more than 180°, the terminal side is 35° counterclockwise past the negative x-axis.

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Example 1 Draw Angles in Standard Position b. Because 410° is 50° more than 360°, the terminal side makes one whole revolution counterclockwise plus 50° more. c. Because 60° is negative, the terminal side is 60° clockwise from the positive x-axis. –

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Checkpoint Draw Angles in Standard Position Draw an angle with the given measure in standard position. ANSWER 30° 1. –

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Checkpoint Draw Angles in Standard Position Draw an angle with the given measure in standard position. ANSWER 460° 2.

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Checkpoint Draw Angles in Standard Position Draw an angle with the given measure in standard position. ANSWER 230° 3.

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Checkpoint Draw Angles in Standard Position Draw an angle with measure 90° in standard position. On a different coordinate grid, draw an angle with measure 90° not in standard position. ANSWER 4.

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Example 2 Find Coterminal Angles SOLUTION There are many correct answers. Choose a multiple of 360° to add or subtract. Find one positive angle and one negative angle that are coterminal with the given angle. a.b.395°45° – a. = 45° – 360° + 315° = 45° – 360° – 405° –

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Example 2 Find Coterminal Angles b. = 395°360° – 35° = 395°360° – 325° ( ( 2 –

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Checkpoint Find one positive angle and one negative angle that are coterminal with the given angle. 5.50° Find Coterminal Angles ANSWER 410°, 310° – 6.375° ANSWER 290°, 430° – 7.70° – ANSWER 15°, 345° –

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Example 3 Evaluate Trigonometric Functions Given a Point SOLUTION Use the Pythagorean theorem to find the value of r. Let be a point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of. () 4, – 3 = r = 4242 + ()2)2 3 – x 2x 2 y 2y 2 + = 25 = 5 Find the value of each function using x 4, y 3, and r 5. == – = = r y sin = 5 3 – = r x cos = 5 4 = x y tan = 4 3 –

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Checkpoint Evaluate Trigonometric Functions Given a Point ANSWER = sin 5 4, = cos 5 3 –, = tan 3 4 – 8. Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of. () 3, 4 –

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Checkpoint Evaluate Trigonometric Functions Given a Point ANSWER = sin 5 4, = cos 5 3, = tan 3 4 9. Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of. () 6, 8

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Checkpoint Evaluate Trigonometric Functions Given a Point ANSWER = sin, = cos, 17 8 – 15 = tan 8 15 – 10. Use the given point on the terminal side of an angle in standard position. Evaluate the sine, cosine, and tangent functions of. – () 158,

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Example 4 Trigonometric Functions of a Quadrantal Angle Evaluate the sine, cosine, and tangent functions of 180°. = SOLUTION When 180°, you know that x r and y 0. = – == = r y sin = r 0 = 0 = r x cos = r r– = 1 – = x y tan = r 0 – = 0

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Example 5 Positive and Negative Trigonometric Functions Determine whether the sine, cosine, and tangent functions of the given angle are positive or negative. a. b.c. d.

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Example 5 Positive and Negative Trigonometric Functions SOLUTION Because the terminal side lies in Quadrant II, sin 100° is positive, cos 100° is negative, and tan 100° is negative. a. Because the terminal side lies in Quadrant I, sin 75° is positive, cos 75° is positive, and tan 75° is positive. b. Because the terminal side lies in Quadrant III, sin 210° Is negative, cos 210° is negative, and tan 210° is positive. c. Because the terminal side lies in Quadrant IV, sin 320° is negative, cos 320° is positive, and tan 320° is negative. d.

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Checkpoint Positive and Negative Trigonometric Functions ANSWER sin 90° 1, cos 90° 0, tan 90° is undefined == Determine whether the sine, cosine, and tangent functions of the angle are positive or negative. 12. 40° ANSWER all positive 11.Evaluate the sine, cosine, and tangent functions of 90°. =

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Checkpoint Positive and Negative Trigonometric Functions Determine whether the sine, cosine, and tangent functions of the angle are positive or negative. 13. 150° ANSWER The sine is positive, the cosine is negative, and the tangent is negative. 14. 225° ANSWER The sine is negative, the cosine is negative, and the tangent is positive.

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VOLLEYBALL players spike the ball at speeds up to 100 miles per hour to prevent the opponent from being able to return the ball.

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