5.3 Trigonometric Functions of Any Angle Tues Oct 28 Do Now Find the 6 trigonometric values for 60 degrees

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 Positive angles rotate counter-clockwise Negative angles rotate clockwise The ray at the end of the rotation is the terminal side

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

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

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

Ex Find the complement and supplement of degrees

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

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

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

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

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

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

5.3 Trig Functions of any Angle Wed Oct 29 Do Now Given that tan B = 5, and B is in the first quadrant, find the other 5 trig values

HW Review: p.471 #

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

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

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

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, 225, 240, 300, 315, 330 deg

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

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)

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