Would someone help me one these two question regarding trigonometry?

Question

Hello,

Here's how it goes: Solve the following trigonometric equations .Give all positive values of the angle between 0* and 360* that will satisfy each.Give any approximate value to the nearest minute only.

1.) 3 sin (theta) - 4 cos (theta) = 2
tan (x+15*) = 3 tan x

2.) tan (x+15*) = 3 tan x


Please give a detailed answer form.

Thanks!!!

Answer 1

1. x = 76.708 deg = 76 deg 46 min 30 sec

I assume you want me to solve this

3*sin(x)-4*cos(x)=2

and that the rest of Equation 1 is a cut and paste error.

3*sin(x)-4*(1-sin(x)^2)^0.5 = 2

You can square this and solve for sin(x). You get the following

x = asin(6/25+4/25*21^0.5)= 76.708 deg

2. x = 8.087 deg = 8 deg 5 min 13 sec

tan (x+15*) = 3 tan x

I am in just a bit of a hurry, so I will be very brief.

tan(x+15 deg)=
(tan(x)+tan(15deg))/(1-tan(x)*tan(15deg))
=3*tan(x)

You can now solve this for tan(x). It is a bit complicated, but you can solve it to get a complicated expression.

Answer 2

1. Something is rotten with this equation. Do you mean that all angles are "x".

2. I know there is some Tan (x+y) equation floating around somewhere, and you would probably use this. For approximate answers, you are looking for x around 70 and 250 degrees as answers.