Question

Find the solution to the follow trig equations on the interval [0,2pi). Round to the nearest ten thousandth. If there are multiple values, enter your answers from least to greatest separated by commas without spaces. Example: .1234,.5678,.9101

1) tan(3x)=1

2) 3sec^2x=4

Answer 1

tan(3x)=1
Let p=3x

Tanp=1

P=tan-¹(1)

P=π/4=45°

Where
P=3x
Tan has a period of π

3x=π/4+πn

X=π/12+πn/3

Where n represent integer

Similar

3sec^2x=4

3/cos²x=4

Cos²x=3/4

Cosx=√3/2=30° or π/6

Cos has a period movement of 2π

x=π/6+2nπ

What ever you do make sure you don't exceed 2π

If you fancy degree (π=180)

Answer 2

I find these are easiest done this way:

tan(3x)=1
I know that tan 45° =1 or tan225° = 1, (using the CAST rule)
3x = 45° or 3x = 225°
x = 15° or x = 75°
but the period of tan(3x) is 360/3 = 120°

so to find a new solution all we have to do is add 120° to any current solution
to stay within the 0 ≤ x ≤ 2π domain
x = 15°, 135°, 255°, 75°, 195°, or 315°
or in radians, π/12, 9π/12, 17π/12, 13π/12, 21π/12

3sec^2x=4
sec^2x=4/3
secx = ± 2/√3 , so x can be in all 4 quadrants
cosx = √3/2 , recognize x = 30°
x = 30°, 150°, 210°, or 330°
or the equivalent radians of π/6, 5π/6, 7π/6 and 11π/6

Answer 3

Cool I like the way you think smart .......you make maths fun to learn here