# Math Help - Trig Graphs and Equations

1. ## 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?

2. 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.

3. 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?

4. 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?

5. ## 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