Trigonometry Flashcards
What are the exact values for sine?
30 degrees or pi/6 = 1/2
45 degrees or pi/4 = root 2/2
60 degrees or pi/3 = root 3/2
What are the exact values for cosine?
30 degrees or pi/6 = root 3/2
45 degrees or pi/4 = root 2/2
60 degrees or pi/3 = 1/2
What are the exact values for tan?
30 degrees or pi/6 = 1/root3
45 degrees or pi/4 = 1
60 degrees or pi/3 = root 3
How would you answer a question phrased as following:
Solve sinx =1/2 for 0<360
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
How would you answer a trig question with a number in front of the sin/cos/tan?
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
How would you answer a trig question with a value in front of the x term?
(e.g. sin2x=1)
Calculate sin/cos/tan of value
Consult CAST for usable quadrants
Find x values BY 2x= _ x=_/2
Write as a solution set
How would you answer a trig question with another term on the left hand side?
(e.g. sinx +1)
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
What do you do if a trig question is asked in radians?
Convert to degrees for easy working then convert back for answers
What value is pi?
180 degrees
How would you answer a trig question which had brackets?
e.g. tan(x-20)
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
What do you do is there is a value in front of an x in brackets?
(e.g. cos(2x-10))
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
What is the compound angle rule for sine?
sin(A+-B) = sinAcosB +- cosAsinB
If positive on LHS, positive on RHS
If negative on LHS, negative on LHS
(Same sign)
What is the compound angle rule for cosine?
cos(A+-B) = cosAcosB -+ sinAsinB
If LHS positive, RHS is negative
If LHS negative, RHS is positive
(Difference signs)
How would you answer a compound angle question?
Usually asked as expand, show that or find the exact value of cos(a+60)
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
What are the two trig identities?
tanx = sinx / cosx
sin^2x + cos^2x = 1
How would you answer compound angle question that involves “acute angles”?
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
How would you confirm the trig identities in a question?
Start with the LHS and expand and simplify until RHS is achieved
How do you recognise a double compound angle formula (dcaf) question?
Will mention cos2x or sin2x
How would you answer a dcaf question that gives a value for tan?
Look for an acute angle in the boundaries
Draw a triangle and annotate sides
What are you being asked to do in double compound angle formulae?
Find the exact values of sin/cos
How would you find the exact values in a double angle question?
Substitute in dcaf and rearrange to find wanted trig(sin or cos)
Solve for sinx or cosx
When is the double angle formula used?
When dealing with sin2x or cos2x
Or when two formulae are present
How would you answer a question asked like the following?
Solve sin2x = -sinx for 0
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
