trigonometry || math
Exercise - Sin or Cos 1
if (int_count_times_randomized <= 1){ //>
return 10;
} else {
return random_min_max_precision(10, 15, 0); //defined in setup_exercise_all.js
}
if (int_count_times_randomized <= 1){ //>
return 30;
} else {
return random_min_max_precision(20, 70, 0); //defined in setup_exercise_all.js
}
if (int_count_times_randomized == 0){
return true;
} else if (int_count_times_randomized == 1){
return false;
} else {
return (Math.random()>0.5); //Half the time ~boolean_adjacent~ is true, the other is false.
}
if (int_count_times_randomized <= 1){ //>
return 0;
} else {
return Math.random()*2*Math.PI;
}
return (true);
Hypotenuse: $h = ~r~$
Angle: $\theta = ~theta~^\circ$
Hint: Does the red side touch the angle?
Yes $\rightarrow$ adjacent side $\rightarrow$ use $\cos\theta$.
No $\rightarrow$ opposite side $\rightarrow$ use $\sin\theta$.
Yes $\rightarrow$ adjacent side $\rightarrow$ use $\cos\theta$.
No $\rightarrow$ opposite side $\rightarrow$ use $\sin\theta$.
Solution
Since the red side [[return (~boolean_adjacent~)?"touches" : "does not touch"]] the angle, it is the [[return (~boolean_adjacent~)?"adjacent" : "opposite"]] side.Recall the rules: adjacent $\rightarrow$ $\cos$, opposite $\rightarrow$ $\sin$.
$l = h [[return (~boolean_adjacent~)? String.raw`\cos`: String.raw`\sin`]] (\theta) = [[return ~r~]] [[return (~boolean_adjacent~)? String.raw`\cos`: String.raw`\sin`]] ([[return ~theta~]]^\circ ) = [[return (~boolean_adjacent~)? (~r~ * Math.cos(~theta~ * Math.PI/180)).toFixed(2) : (~r~ * Math.sin(~theta~ * Math.PI/180)).toFixed(2) ]]$.
$~r~ \cos ~theta~^\circ$
[[
if (~boolean_adjacent~) {
return "Correct. The red side touches the angle so it is the adjacent side."
} else {
return "Incorrect. The red side does not touch the angle so it is the opposite side."
}
]]
$~r~ \sin ~theta~^\circ$
[[
if (~boolean_adjacent~) {
return "Inorrect. The red side touches the angle so it is the adjacent side."
} else {
return "Correct. The red side does not touch the angle so it is the opposite side."
} ]]
if (~boolean_adjacent~) {return 0} else {return 1}