Trigonometry

Question 1

What are the exact values for sine?

Answer 1

30 degrees or pi/6 = 1/2
45 degrees or pi/4 = root 2/2
60 degrees or pi/3 = root 3/2

Question 2

What are the exact values for cosine?

Answer 2

30 degrees or pi/6 = root 3/2
45 degrees or pi/4 = root 2/2
60 degrees or pi/3 = 1/2

Question 3

What are the exact values for tan?

Answer 3

30 degrees or pi/6 = 1/root3
45 degrees or pi/4 = 1
60 degrees or pi/3 = root 3

Question 4

How would you answer a question phrased as following:

Solve sinx =1/2 for 0<360

Answer 4

do sine inverse of a half
x=30
Consult CAST diagram and chose which quadrants would give a positive answer
for sine, sine and all
Use quadrant rule to find values of x

Question 5

How would you answer a trig question with a number in front of the sin/cos/tan?

Answer 5

Take it to the other side of the equal sign and divide
Calculate sin/cos/tan of value
Consult CAST for usable quadrants
Find x values
Period = top boundary(360)/no. in front of sin/cos/tan
Add/Subtract x values to the period until answer exceeds boundary
Write as a solution set

Question 6

How would you answer a trig question with a value in front of the x term?
(e.g. sin2x=1)

Answer 6

Calculate sin/cos/tan of value
Consult CAST for usable quadrants
Find x values BY 2x= _ x=_/2
Write as a solution set

Question 7

How would you answer a trig question with another term on the left hand side?
(e.g. sinx +1)

Answer 7

Take over the equals sign
Solve for x as usual (don’t put in a negative sign if present)
If RHS is negative, chose opposite quadrants
Find x values
Write as a solution set

Question 8

What do you do if a trig question is asked in radians?

Answer 8

Convert to degrees for easy working then convert back for answers

Question 9

What value is pi?

Answer 9

180 degrees

Question 10

How would you answer a trig question which had brackets?

e.g. tan(x-20)

Answer 10

Find x value as normal using CAST
Place bracket on LHS when finding x values
(e.g. x-20=180+value)
Rearrange to find x
Write as a solution set

Question 11

What do you do is there is a value in front of an x in brackets?
(e.g. cos(2x-10))

Answer 11

Find x value as normal
Put bracket on LHS of Quadrant equation to find x
Use value in front of x to find the period

Question 12

What is the compound angle rule for sine?

Answer 12

sin(A+-B) = sinAcosB +- cosAsinB
If positive on LHS, positive on RHS
If negative on LHS, negative on LHS
(Same sign)

Question 13

What is the compound angle rule for cosine?

Answer 13

cos(A+-B) = cosAcosB -+ sinAsinB
If LHS positive, RHS is negative
If LHS negative, RHS is positive
(Difference signs)

Question 14

How would you answer a compound angle question?

Usually asked as expand, show that or find the exact value of cos(a+60)

Answer 14

Expand brackets using rules/formula
Sub in given value (can be radians or an angle)
Use exact values table or calculator to find values
If expand, leave in simplest form
If show that, make sure RHS value=LHS value
If exact value, simplify as far as possible

Question 15

What are the two trig identities?

Answer 15

tanx = sinx / cosx

sin^2x + cos^2x = 1

Question 16

How would you answer compound angle question that involves “acute angles”?

Answer 16

Draw triangle
Use soh cah toa to label sides from information given
Find sin and cos from each triangle through soh cah toa
Work out LHS and RHS by using formula

Question 17

How would you confirm the trig identities in a question?

Answer 17

Start with the LHS and expand and simplify until RHS is achieved

Question 18

How do you recognise a double compound angle formula (dcaf) question?

Answer 18

Will mention cos2x or sin2x

Question 19

How would you answer a dcaf question that gives a value for tan?

Answer 19

Look for an acute angle in the boundaries

Draw a triangle and annotate sides

Question 20

What are you being asked to do in double compound angle formulae?

Answer 20

Find the exact values of sin/cos

Question 21

How would you find the exact values in a double angle question?

Answer 21

Substitute in dcaf and rearrange to find wanted trig(sin or cos)
Solve for sinx or cosx

Question 22

When is the double angle formula used?

Answer 22

When dealing with sin2x or cos2x

Or when two formulae are present

Question 23

How would you answer a question asked like the following?

Solve sin2x = -sinx for 0

Answer 23

Get rid of 2x by substituting in dcaf
Bring over -sinx to make it positive
Factorise
Set =0
Find values using graphs and CAST
Write out a solution set