IB Math SL 10-13

Name:________________

Ticket in the door-Self assess for success!

Answer the following without using your notes!

(a) Show that 4−cos2 A+5 sin A=2sin2 A+5 sin A+3 (2)

(b) Hence, solve the equation 4−cos2 A+5=0 for 0≤θ≤2π , (5)

How would you describe yourself? Circle one!

I feel very confident, this was easy for me.

I feel O.K I’m still making errors when I use the identities.

I feel OK, but I’m making errors when I use the unit circle.

Name ___________________________ 10-13 NotesIB Math SL

Lesson 10-13 Application of trig functions-IB exam

Learning Goals: How do we apply different methods of solving and proving trig functions.

Remember! Trig Masters don't always see exactly how to solve a proof when they first see it, and that

often it comes down to "playing around with it" and trying a few things before you find the path that will get you to the solution. The key is to not give

up if you hit a few dead ends!A guide to solving trig equations

STEP 1: Convert all tan to sin and cos. Most of this can be done using identities.

STEP 2: Collect all like terms on one side of equal signs

STEP 3: Adjust your domain according to problem.

Step 4: Sketch unit circle and angles.

A guide to proving trig identitiesUse only appropriate steps; you don’t need to do every step each time you prove!

STEP 1: Convert all tan to sin and cos. Most of this can be done using identities.

STEP 2: Check for angle multiples (2A or 3A) and remove them using the appropriate formulas.

STEP 3: Expand any equations you can, combine like terms, and simplify the equations.

Don’t forget about rules used with numbers:

Dividing fractions keep change flip

Squaring a binomial double distribute

STEP 5: If you have a 1 – trig function2, try a Pythagorean identity

STEP 6: Try factoring out a GCF if you can

STEP 7: Now, both sides should be exactly equal, or obviously equal, and you have proven your identity.

Theme of the Unit:

Productive Struggle!

Name: 11-13 Practice A

The basics:

1. Use your knowledge of the unit circle to solve for all values of θ in the interval

sin θ=−12

2. Use your knowledge of the unit circle to solve for all values of θ in the interval 0≤θ≤2π .

tanθ=−1

3. sin ¿ ; 0≤ x<2 π

4. Let f (x )=tan2 x−tan 2 x sin2x 0≤ x<2 π

a) Show that Let f (x )=sin2 x .

b) Hence solve f ( x )=12 for 0≤ x<2 π

Any common factors? Do you see any squares? Can you sub in any identities? Simplify algebraically.

What is the VALUE of the function? What reference Angle gives me that

value? What sign is the value- what

quadrant/ should you focus on?

What do we do when we see a non-single angle?

Now you are ready to apply!

Name: 11-13 Practice B