Hello my name is Gerald and this is my scribe post for the lesson we had today. First off Mr. K put questions on to the board for us to do.
Solve each equation
a) csc x = 2.3 ; 0° <>
solution: cosecant is the recprical of sine
sin x = 1 / 2.3
Arc sin (sin x) = Arc sin (1 / 2.3)
= Arc sin(1 / 2.3) or x = sinֿ¹ (1 / 2.3 )
and after plugging that onto your calculator IN DEGREES
answer:
x = 25.8° in quadrant I
x = 154.2° in quadrant II - why? because 180° - 25.8° = 154.2°
b) 2 tan² x + 5 tanx - 3 = 0 ; x £ r
solution: let tan x = a DO NOT EVER DO: let tan x = x
2a ² + 5a - 3 = 0 also be 2a² + 6a - a - 3 = 0 - why? because 6a - a is also 5a
next step is to factor the equation
2a² + 6a - a - 3 = 0
= 2a (a + 3) - 1 (a + 3)
= (2a - 1) (a + 3) = 0
a = - 3 tan x = - 3a = 1 / 2 tan x = 1 / 2
plug onto your calculator IN RADIANS
Arc tan - 3 = x or tanֿ¹ - 3 = x
x = - 1.2490
answer: 0.4636 + 2kπ ; kei
SKETCH EACH GRAPH
f(x) = 2sin x -1
g(x) = - cos + 2
Mr K. then made us find the similarities and differences of these 2 graphs. Finding the similarities and differences has helped us understand the graphs and equations more fully.
