4.4 – Trigonometric Functions of any angle

What can we infer?? *We remember that from circles anyway right??? So for any angle….

Let’s do some examples… Ex. 1 – If (-3, 4) is a terminal point, Find sin θ, cos θ, and tan θ.

Example 2: Let (-2, -5) be the terminal point, find all six trig functions.

Evaluating Trig Functions Given and cos θ >0, find sin θ and secθ. Given and θ in Quad II, Find tan θ, csc θ, sin θ

Reference Angles If θ is an angle in standard position, the reference angle is the acute angle θ formed by the terminal side of θ and the x axis (horizontal axis). Simple definition: the angle formed by the HORIZONTAL and terminal side!!

Finding Reference Angles:

Solution to (b.) :

Let’s practice some more… Try example 4: a, b, and c on page 293.

4.4 Day 1 Homework Pg. 297 #’s 1, 3, 7, 11 – 41 odd

Day 2 – Warm UP Pg. 297 #’s 4, 12, 14, 18, 32, 36, 38, 42

Evaluating Trig Functions at Any Angle: *It might be easier to switch steps 2 and 3!

Use reference angles to evaluate the folllowing trig functions:

Now with radians:

Let’s practice… Pg. 297 #’s 38 – 44 even.

Using Trig Identities to Solve Trig Functions: EX. Let θ be an angle in Quadrant II such that sin θ = 1/3. Find the cos θ. *What identity should we use? *Remember the angle is in Quadrant II

Now lets find the tan θ. *What identity should we use? *Remember to check your sign! Let’s practice some more on page 298 #’s even

Using a Calculator: To evaluate or solve a trig function of any angle, the same rules apply! REMEMBER TO BE IN THE CORRECT MODE!! Steps to refresh your memory are on pg. 296…. Lets make sure we can do Example 7!

4.4 DAY 2 - Homework Pg. 297 #’s odd, 61, 65, odd, 85, 89, 93

Quiz Review…. No calculator/ no unit circle Pg. 297 #’s 1, 10, 16, 20, 24, 30, 36, 46, 50, 54, 58, 62, 66, 70, 72, 76, 78, 82, 90, 91, 94, 96