A-level Maths- Trigonometry and Circular Measures 1
What is sin(180+x) equal to? (2 things)
-sinx and sin(-x)
What is the period of sinx?
360 degrees
Give the equation for the area of a sector, where theta (the angle within the sector) is in radians
A = 1/2*r^2*theta
What are the amplitude and period of the functions y=acosbx and y=asinbx?
Amplitude a, period 2*pi/b
How should you convert degrees to radians?
Divide by 180 and multiply by pi
How do you convert from radians to degrees?
Divide by pi and multiply by 180
If you have a factor of sinx on both sides of an equation, what must you NOT do?
Divide by sinx. You will "lose solutions" if you do this
If you had the equation tanx = 0.6, how would you use that to find all the values within a certain range?
Do tan^-1(0.6) and add or subtract multiples of 180 (the period of tan is 180)
What should you try to do if there is more than one trigonometric function in an equation?
Eliminate one of them, perhaps using trig identities
What are three things you can do when an equation cannot easily be changed to be in the form trigonometric function = constant?
Look for quadratic equations, take everything over to one side and factorise or use trig identities
Where does sin^2x + cos^2x = 1 come from?
Pythag of the unit circle
How can you form inverse functions using trigonometric functions?
Reflect them in the line y = x
What must you remember to do when solving sin2x = 0.6 through substitution of 2x for A?
To change the limits accordingly (multiply them by 2 in this case)_ and convert back to the original variable at the end
How do you solve equations such as sin2x = 0.6?
Use a substitution such as A = 2x
How do you relate cos to sin?
Using sin^2x + cos^2x =1
How else (other than graphically) can sine and cosine functions be represented?
Using the unit circle
If you had the equation sinx = 0.6, how would you use that to find all the values within a certain range?
Work out sin^-1(0.6) = 36.9, subtracting from 180 (this gives the value on the far side of the sine "hump") and adding or subtracting 360 to either of these two solutions until you've found all the solutions. Draw a graph always
If you had the equation cosx = 0.6, how would you use that to find all the values within a certain range?
You would do cos^-1(0.6), multiply by -1 (to find the solution on the other side of the cos "hump") and then add or subtract 360 to these solutions until all have been found. Draw a graph always
What is cosx equal to? (2 things)
cos(-x) and cos(x+360)
What is cos(180-x) equal to? (2 things)
cos(180+x) and cos(-x)
What is cos(x-90) equal to? (2 things)
cos(90-x) and sinx
Give the equation for the length of an arc, where theta (the angle that subtends the arc) is in radians
l = r*theta
What is sinx equal to? (2 things)
sin(180-x) and sin(x+360)
What is sin(x+90) equal to? (2 things)
sin(90-x) and cosx
