# Trig Graphs and Equations

• Sep 22nd 2008, 11:07 PM
Brownhash
Trig Graphs and Equations
Can anyone please provide the answers to these questions as this is due tomoroow. Any help would be much appreciated thanks.

(1) Solve:
(a) 2sinx = 0.2, 0o ≤ x ≤ 360o
(b) sinx + 3 = 3.5, 0 ≤ x ≤ 2π
(c) 3sin2x = 0.8, 0o ≤ x ≤ 360o
(d) sin(x – 90o) = 0.3, -180o ≤ x ≤ 180o
(e) 2sinx + 3 = 2, 0 ≤ x ≤ 2π.

(2) Solve the following trigonometric equations:
(a)tan(theta) = -1.3, 0(degrees)
(b) cos(theta) +3 = 3.1
(c)14sin(theta) = 10

(3) The fans on a windmill rotate at a constant speed.
P is the point at the end of the fan.
The height, h m, of P above the ground
at time t seconds is given by the equation:
h = 24 + 15sin t , t is measured in radians.
(a) How long does it take the point P to move from the top to the bottom of the arc?
(b) What proportion of a cycle is the point P above 30 metres?
• Sep 22nd 2008, 11:10 PM
Jameson
Are calculators allowed?

For most of 1) and 2), you need to solve the equations so that you get "trig function (x) = A", where trig function is sine, cosine, whatever and then you use the trig inverse to solve for the angle. On your calculator, it looks like $\sin^{-1}(x)$ or something similar.
• Sep 22nd 2008, 11:16 PM
Brownhash
Yes we are allowed calculators.
Would you be able to please show me one of the questions so i get the idea and can do the rest?
• Sep 22nd 2008, 11:18 PM
Jameson
Sure.

1(a). 2sinx = .2
sinx = .1

$x = \sin^{-1}(.1)$

In words...
x = the sine inverse of .1.

I don't have a calculator handy. Do you see how it's done?
• Sep 23rd 2008, 06:25 AM
andrew
Response to Brownhash
Trig Graphs and Equations
Can anyone please provide the answers to these questions as this is due tomoroow. Any help would be much appreciated thanks.

(1) Solve:
(a) 2sinx = 0.2, 0o ≤ x ≤ 360o
(b) sinx + 3 = 3.5, 0 ≤ x ≤ 2π
(c) 3sin2x = 0.8, 0o ≤ x ≤ 360o
(d) sin(x – 90o) = 0.3, -180o ≤ x ≤ 180o
(e) 2sinx + 3 = 2, 0 ≤ x ≤ 2π.

(2) Solve the following trigonometric equations:
(a)tan(theta) = -1.3, 0(degrees)
(b) cos(theta) +3 = 3.1
(c)14sin(theta) = 10

(3) The fans on a windmill rotate at a constant speed.
P is the point at the end of the fan.
The height, h m, of P above the ground
at time t seconds is given by the equation:
h = 24 + 15sin t , t is measured in radians.
(a) How long does it take the point P to move from the top to the bottom of the arc?
(b) What proportion of a cycle is the point P above 30 metres?

Response by Math genius
One way to solve question one is the use of general formulars:
The one for sin x = a is x = 180n +(-1)^n x p where p = sin-1 a
The one for cos x = a is x = 360n + p where p = cos-1 a
The one for tan x = a is x = 180n + p where p = sin-1 a
n = 0,1,2,3,.... untill all angles in range are exhausted... try this