trigonometry Flashcards
how to solve this question
how to solve this question
how to solve this question
to find the other solutions when solving a trig function for sin
180 - x
to find other solutions when solving a trig function for cos
360 - x and 360 + x
to find other solutions when solving a trig function for tan
180 + x
how to solve this question
how to solve this question
steps:
1) hidden quadratic so sub sin = y
2) solve for y and factorise
3) replace y with sin again and solve for x
what is a trig identity linkig sin and cos = 1
what is a trig identity linking sin and cos to tan
sin and cosec graph
cos and sec graph
tan and cot graph
what are 2 Pythagorean identities
cot and cosec pythagoream identity
1 with a cot is cosy
tan and sec pythagoream identity
1 with a tan is secsy
prove that
what has to happen for us to have inverse functions (draw it on a graph)
1-to-1 mapping
how to do the domain and range of arcsin
steps:
1) must have 1-to-1 mapping so restrict domain of sin to pie/2 and -pie/2
2) range would be -1 and 1 for sin
3) for arc sin switch the domain and range around
how to do the domain and range of arccos
steps:
1) must have 1-to-1 mapping restrict domain of cos to 0 and pie
2) the range would be 1 and -1
3) for arccos switch the domain and range around
how to do the domain and range of arctan
steps:
1)must have 1-to-1 mapping so restrict the domain to pie/2 and -pie/2
2) the range won’t exist as it is an asymptote and won’t intercept the y values
3) for arctan switch the domain and range so the domain would be XER
what are the 3 trignometric identities
manipulating trig identities
manipulating trig identities (3 ways to write the cos double angle formula
manipulating trig identities
how to do this question
steps:
1) use the sin double angle formula
2) calculate the trig with B in it as they are an actual answer and not x
3) solve for x
how to do a harmonic form question (R-method)
steps:
1) use the double angle formula on the RHS
2) set the LHS cos = RHS cos and same for sin
3) find R using Pythagoras
4) divide the sin function by the cos one
5) you get tan and solve for alpha
PART B
1) use the RHS answer of the last question
2) solve like a normal trig question
what is the minimum for this (harmonic form)
what is the minimum value for this harmonic form
denominator needs to be the biggest to make the smallest value (minimum)
how to solve a and b of this harmonic form question
steps:
1) sin double angle formula on the RHS
2) set the 5 to sin and 12 to cos
3) find R
4) put 5/12 = tanx
5) solve for x
PART B
1) work out the max which is the biggest possible value 13+7
2) the minimum would be -13 + 7 which is -6
what is one key rule for using small angle approximations
small angle approximation for sin
small angle approximation for cos
small angle approximation for tan
small approximation question
steps:
1) use the small approximations for cos and tan
2) expand
3) need to know if x is small (in order to use approximation) x^3 is tiny therefore = 0
how to differentiate sin by first principles
https://youtu.be/1fsvZBy0m3Q?si=80vadC-T8dr7NK84
