Difference between revisions of "Euclid 2020/Problem 6"
(Created page with "(a) Suppose that the function <math>g</math> satisfies <math>g(x) = 2x - 4</math> for all real numbers <math>x</math> and that <math>g^-1</math> is the inverse function of <ma...") |
|||
| Line 3: | Line 3: | ||
<math>g(f(g^-1(x)))</math> = 2x^2 + 16x + 26<math> for all real numbers </math>x<math>. What is the value of | <math>g(f(g^-1(x)))</math> = 2x^2 + 16x + 26<math> for all real numbers </math>x<math>. What is the value of | ||
</math>f(\pi)<math>? | </math>f(\pi)<math>? | ||
| − | (b) Determine all pairs of angles </math>(x; y)<math> with </math>0 \le x < 180<math> and </math> | + | (b) Determine all pairs of angles </math>(x; y)<math> with </math>0<math> </math>\le x<math> </math><<math> </math>180<math> and </math>0<math> </math>\le y<math> </math><<math> </math>180<math> that |
satisfy the following system of equations: | satisfy the following system of equations: | ||
</math>log_2(sin x*cos y)<math> = -3/2</math> | </math>log_2(sin x*cos y)<math> = -3/2</math> | ||
<math>log_2(sin x/cosy)</math> = 1/2$ | <math>log_2(sin x/cosy)</math> = 1/2$ | ||
Revision as of 03:29, 31 March 2023
(a) Suppose that the function 
satisfies 
for all real numbers 
and
that 
is the inverse function of . Suppose that the function 
satisfies
= 2x^2 + 16x + 26
x
f(\pi)
(x; y)
0$$ (Error compiling LaTeX. Unknown error_msg)\le x$$ (Error compiling LaTeX. Unknown error_msg)<$$ (Error compiling LaTeX. Unknown error_msg)180
0$ $ (Error compiling LaTeX. Unknown error_msg)\le y$$ (Error compiling LaTeX. Unknown error_msg)<$$ (Error compiling LaTeX. Unknown error_msg)180$ that
satisfy the following system of equations:$ (Error compiling LaTeX. Unknown error_msg)log_2(sin x*cos y)
= 1/2$
