5.3 Trigonometric Functions of Any AngleTues Oct 28

Do NowFind the 6 trigonometric values for 60

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

• 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 71.46 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, 71-77 odds

5.3 Trig Functions of any AngleWed 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 #1-37 71-77

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, 270 360

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, 83-105 odds