Simple trig? (1 Viewer)

[enigma_1]

How do I do this? Sorry been long since I last touched trig Just need someone to jog my memory, cheers.

Solve this equation for 0<= x <=360 degrees.

tanx = (root2) -1

 

[HeroicPandas]

x = arctan(sqrt(2) - 1) = very hard

The problem is that disgusting square root of 2..

I have an idea, let's eliminate that square root by first isolating it and then squaring both sides!

(root2) = tanx + 1 (isolate root2)

2 = (tanx)^2 + 2tanx + 1 (squaring both sides)

(tanx)^2 + 2tanx - 1 = 0 (re-arrange)

Then solve quadratic

 

[braintic]

x = arctan(sqrt(2) - 1) = very hard

The problem is that disgusting square root of 2..

I have an idea, let's eliminate that square root by first isolating it and then squaring both sides!

(root2) = tanx + 1 (isolate root2)

2 = (tanx)^2 + 2tanx + 1 (squaring both sides)

(tanx)^2 + 2tanx - 1 = 0 (re-arrange)

Then solve quadratic

Its not hard at all - simply use your calculator.

arctan(sqrt 2 - 1) = 22.5 degrees

sqrt 2 - 1 is positive, and the other quadrant in which tan is +ve is the 3rd.

x=22.5 and (180+22.5)

No need for a quadratic equation. The quadratic gives unwanted solutions anyway.

 

[QZP]

he got you

 

[HeroicPandas]

Its not hard at all - simply use your calculator.

arctan(sqrt 2 - 1) = 22.5 degrees

sqrt 2 - 1 is positive, and the other quadrant in which tan is +ve is the 3rd.

x=22.5 and (180+22.5)

No need for a quadratic equation. The quadratic gives unwanted solutions anyway.

I realized that when you solve the quadratic, you end up with tanx = 1 + root2 lol

 

[braintic]

I realized that when you solve the quadratic, you end up with tanx = 1 + root2 lol

I didn't think of that either - it should have been obvious to me.