trig (1 Viewer)

[vanush]

How do you solve sin x = 2/5 without a graph?

 

[dddman]

x = sin^-1(2/5) = 23.57Deg or .13pi Rads

 

[vanush]

sine inverse 2/5 gives .13pi c.. but how do you find the other point (because the question asks for values between 0 and 2pi)

 

[pLuvia]

Since sinx is positive in the first and second quadrant then
sinx=2/5
x=sin^-1(2/5) and 180-sin^-1(2/5)
=23.58 and 156.42

 

[vanush]

o yeah
lol

 

[vanush]

Show, with a diagram, that

cos (3pi/2 + theta) = sin theta

 

[alcalder]

Graph

y = sin (theta)

y = cos(3pi/2 + theta) = cos(theta - (-3pi/2))

The second curve is just cos(theta) shifted 3pi/2 to the left.

You will see that the graphs for both equations are the same.

Is that what you were wanting??

 

[vanush]

yes, but i was thinking you had to show it using the astc diagram

because the exercise it is in is before graph drawing

 

[Riviet]

Using the diagram,
cos(3pi/2 + θ)=cos[2pi - (pi/2 - θ)]
=cos(pi/2 - θ) since cos is positive in first and fourth quadrants, ie cos(2pi-A)=cosA
=sinθ