See also:
What’s the easiest way to answer a question about mutliple trigonometry solutions??
Draw an accurate graph.
After how many degrees does $\sin(\theta)$ repeat??
$$ 360^{\circ} $$
After how many degrees does $\cos(\theta)$ repeat??
$$ 360^{\circ} $$
After how many degrees does $\tan(\theta)$ repeat??
$$ 180^{\circ} $$
When drawing a $\tan$ graph, what should you sketch first??
The asymptotes.
Where are the asymptotes on a $\tan$ graph, in degrees??
Start at $90^\circ$ and then repeat every $180^{\circ}$.
What is the value of $\sin$ at the origin??
$$ 0 $$
What is the value of $\cos$ at the origin??
$$ 1 $$
What is the value of $\tan$ at the origin??
$$ 0 $$
How could you write $\tan\theta$ in terms of $\sin$ and $\cos$??
$$ \frac{\sin\theta}{\cos\theta} $$
If $\cos 90^{\circ}$ is zero, why is $\tan 90^{\circ}$ undefined??
Because $\tan\theta = \frac{\sin\theta}{\cos\theta}$ and you can’t divide by $0$.
How could you write the length of the opposite side?
How could you write the length of the adjacent side?
This diagram shows a triangle where $\theta$ is approaching $0$. What is the value of $\cos\theta$ approaching??
$$ 1 $$
This diagram shows a triangle where $\theta$ is approaching $0$. What is the value of $\sin\theta$ approaching??
$$ 0 $$
This diagram shows a triangle where $\theta$ is approaching $90^{\circ}$. What is the value of $\cos\theta$ approaching??
$$ 0 $$
This diagram shows a triangle where $\theta$ is approaching $90^{\circ}$. What is the value of $\sin\theta$ approaching??
$$ 1 $$
What proportion of the hypotenuse is the opposite side??
$$ \sin\theta $$
If your calculator gives you $x$ as a solution to $\sin^{-1}$, what are the three other solutions??
$$ 180 - x $$
$$ -180 - x $$
$$ -360 + x $$
If your calculator gives you $x$ as a solution to $\cos^{-1}$, what are the three other solutions??
$$ 360 - x $$
$$ -x $$
$$ -(360 - x) $$
$\cos^{-1}$ has solutions $x$ and $360 - x$. Because $\cos\theta = \cos-\theta$, what are the other two solutions??
$$ -x $$
$$ -(360 - x) $$
If your calculator gives you $x$ as a solution to $\tan^{-1}$, what are the other two solutions??
$$ x + 180 $$
$$ x - 180 $$
How could you find one solution of $\sin(2\theta) = 0.1$??
$$ \frac{\sin^{-1}(0.1)}{2} $$
How could you find one solution of $\sin(\theta + 30^{\circ}) = 0.1$??
$$ \sin^{-1}(0.1) - 30^{\circ} $$
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date: 2020-11-25 16:36
tags:
- '@?maths'
- '@?public'
title: Maths - Multiple Trig Solutions