Math Is Fun Forum

tyuighp

Member

Registered: 2015-12-04

Posts: 12

Find all angles θ

Find all angles θ in [0, 2π) for which
sin θ + cos θ + tan θ + cot θ + sec θ + csc θ = 6.4

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Find all angles θ

Sin2θ = -1, 0.96, 26

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find all angles θ

hi NakulG

I hadn't got anywhere with this.  Please would you give a few hints/.  Thanks

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Find all angles θ

sinθ + cos θ = x and sinθcosθ=y
substituting we get
x^3 - 6.4x^2+x+8.4=0
Solve for x, so x = -1, 1.4 & 6

Hope this helps...

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find all angles θ

hi NakulG

Many thanks for that.  I'll give it a try. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Find all angles θ

:-)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Find all angles θ

hi NakulG

Yep!  Got it now.  That's an inspired substitution!  Thanks once again.  colon bracket with no minus gives a on this forum.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

NakulG

Member

Registered: 2014-09-02

Posts: 186

Re: Find all angles θ