ch7 modelling with trig

Question 1

How to derive addition formula of Sin(a+b)

Answer 1

• Draw out shape with 3 triangles.
• label bottom angle a and one above b.
• label each side.
• then show that the opposite of sin(a+b) is the same as the addition of the side sinacosb+sinbcosa

Question 2

How do you prove the tan addition formula?

Answer 2

Divide the sin addition formula by the cos addition formula.

Sub in the addition formula and then expand and simplify.

Question 3

How can you use the addition formula to calculate sin15=root 4 - root 2/4?

Answer 3

Make sin15 a subtraction of sin(45-30) then sub in these values of a and b into the formula.

Question 4

How can you use the addition formulas to derive the double angle formulas?

Answer 4

Cause the addition or the subtraction to = 2A

and sub this into the addition formula.

Question 5

What to do if you get a sin(3x) and have to solve?

Answer 5

Change it to Sin(2x+x) and sub this into the addition formula then sub in the double angle formula into that.

Question 6

What are the steps to express 3sinx+4cosx into Rsin(x+alpha)

Answer 6

Step 1- use the addition formula to expand Rsin(x+alpha)
Step 2- After this compare the coefficients of sin and cos on both sides.
Step 3- create two simultaneous equations
step 4 -then rearrange to create a right angled triangle.
Step 5- use this to calculate R and theta.

Question 7

What is important when finding solutions when modelling with trig?

Answer 7

Find out how many solutions it is asking for.

May need more than 1 solution.