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5.3 Trigonometric Functions of Any Angle Thurs Jan 2

5.3 Trigonometric Functions of Any Angle Thurs Jan 2. Do Now Find the 6 trigonometric values for 6 0 degrees. 5.1-5.2 Quiz Review. Angles and the Coordinate Plane. When constructing an angle on a coordinate plane (x-y), the initial side is placed on the x-axis with the vertex on the origin

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5.3 Trigonometric Functions of Any Angle Thurs Jan 2

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  1. 5.3 Trigonometric Functions of Any AngleThurs Jan 2 Do Now Find the 6 trigonometric values for 60 degrees

  2. 5.1-5.2 Quiz Review

  3. Angles and the Coordinate Plane • When constructing an angle on a coordinate plane (x-y), the initial side is placed on the x-axis with the vertex on the origin • Positive angles rotate counter-clockwise • Negative angles rotate clockwise • The ray at the end of the rotation is the terminal side

  4. Coterminal Angles • If two angles have the same terminal side, they are considered coterminal angles. Since 360 deg is one full rotation, we add or subtract multiples of 360 to find coterminal angles

  5. Ex • Find 2 positive and negative angles that are coterminal with • 1) 51 deg • 2) -7 deg

  6. Review: Comp and Supp Angles • 2 positive angles are complementary if their sum is 90 degrees • 2 positive angles are supplementary if their sum is 180 degrees

  7. Ex • Find the complement and supplement of 71.46 degrees

  8. Trig functions on angles of rotation • We can construct right triangles on any of the 4 quadrants, where the base is on the x-axis • These are called reference triangles and can be used to find the trig values of angles greater than 90 degrees

  9. Trig functions • Given a reference triangle, the 6 trigonometric functions of any angle are: • Note: these can be negative

  10. The signs of the trigonometric functions • Quadrant 1: All are positive • Quadrant 2: Sin / Csc are positive • Quadrant 3: Tan / Cot are positive • Quadrant 4: Cos / Sec are positive

  11. Ex 3 p.464 • Find the 6 trigonometric function values for each angle (in book)

  12. Ex4 • Given that tan P = -2/3 and P is in the second quadrant, find the other function values

  13. Closure • Given cos A = -4/5 in quadrant 2, find the other 5 trig values • HW: p.471 #1-37 odds, 71-77 odds

  14. 5.3 Trig Functions of any AngleFri Jan 3 • Do Now • Given that tan B = 5, and B is in the first quadrant, find the other 5 trig values

  15. HW Review: p.471 #1-37 71-77

  16. Terminal Side on an Axis • An angle whose terminal side falls on one of the axes is a quadrantal angle. • Since one of the sides must be 0, the hypotenuse must be equal to the other side

  17. Terminal Side on an Axis • Let’s pick a side/hypotenuse of 1, • Find the sin,cos,tan of 90, 180, 270 360 degrees

  18. Ex • Find each of the following: • 1) sin -90 deg • 2) csc 540 deg

  19. Reference Angles • The reference angle for an angle is the acute angle formed by the terminal side of the angle and the x-axis. • This allows us to find exact trig values for 120, 135, 150, 210, 235, 240, 300, 315, 330 deg

  20. Ex • Find the sine, cosine, and tangent values for • 1) 225 deg • 2) -780 deg

  21. Other angles • If an angle is not a quadrantal angle or has a reference angle, we need to use the calculator • Note: Make sure your calculator is on the correct mode! (DEGREES or RADIANS)

  22. Closure • Find the values of sin 90 deg and sec 315 deg • HW: p.472 #39-69 odds, 83-105 odds

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