trigonometry

Question 1

possible questions

Answer 1

• solving trig equations
• sketch trig graphs
• double angle formula
• addition formula
• wave function
• solve the equation with the wave function
• solve the equation using double angle formula
• max and min values

Question 2

sketch trig graphs process

Answer 2

• question form y= asin(bx+c) or y= acos(bx+c)+d
• amplitude=a with verticle shift from ±d
• number of cycles=b and period 360÷b (if b was 4, graph would repeat 4 times)
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• if amplitude asked for, find middle between top and bottom
• if period asked for, do 360÷b(4) which would =90

Question 3

solving trig equation process

Answer 3

• 3sin2x= 1 0<x<360
• sin2x= 1/3 0<2x<720
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• 2x= sin⁻¹ (1÷3)
• 2x= 19.5, 160.5 (here, add 360 if within limits)
• 2x= 379.5, 520.5
• x= 9.75, 80.25, 189.75, 260.25 (divide all answers by whatever is infront of x)

Question 4

how to find x on a triangle

Answer 4

if hypotenuse, then;
*x²= 2²+2²
*x²= 8
*x= √8

Question 5

wave function process

Answer 5

• expand with addition formula
• equate co-efficients
• calculate k
• calculate a
• write in original formula
  ‎
  k(cosx-a)= k[cosxcosa+sinxsina]
  ‎‎‎‎‎‎‎‎‎‎‎‎‎= kcoscoa+ksinxsina
  ‎‎‎‎‎‎‎‎‎‎= 2cosx+3sinx
  ‎
  ‎‎‎‎‎‎‎‎‎‎‎‎‎kcosa= 2
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎ksina= 3
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎k= √2²+3²
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎k=√13
  ‎
  ‎‎‎‎‎‎‎‎‎‎‎‎‎tana= sina/cosa
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎tana= 3/2
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎a=tan⁻¹(1÷3)
  ‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎a= 56.3
  ‎
  ‎‎‎‎‎‎‎‎‎‎‎‎‎√13cos (x-56.3)

Question 6

solve equation with wave function

Answer 6

a) =√41sin (x+0.896)
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b) hence, solve 4sinx+5cosx= 5.5
√41sin (x+0.896)= 5.5
sin (x+0.896)= 5.5/√41
‎
x+0.896= sin⁻¹(5.5÷√41)
x+0.896= 1.033, 2.108
x= 0.137, 1.212

Question 7

max and min values

Answer 7

q: y= 3sin (x-π/3)
‎
3sin (x-π/3)= 3
sin(x-π/3)= 1
x-π/3= 90
x= 5π/6