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Converting Degrees to Radians

rebelmaths

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Convert the following to radians (use \"pi\" for $\\pi$):

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To convert degrees to radians: multiply by $\\pi$ and divide by 180.

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$\\var{d1}^{\\circ}$ = [[0]] radians

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To convert to radians divide by 180 and multiply by $\\pi$

$\\var{d3}^{\\circ}$ = [[0]] radians

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Converting Radians to Degrees

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Convert the following to degrees:

Round your answer to 2 decimal places.

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To convert radians to degrees: multiply by $\\pi$ and divide by 180.

$\\frac{\\var{d1} \\times 180 }{\\pi} = \\var{a1}$

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$\\var{d1}$ radians= [[0]] $^{\\circ}$

$\\frac{\\var{d4}\\pi}{5}$ radians= [[0]] $^{\\circ}$

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Finding the lengths and angles within a right-angled triangle using: pythagoras theorem, SOHCAHTOA and principle of angles adding up to 180 degrees.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Using the right-angled triangle pictured below (not to scale), find the specified side lengths or angles using trigonometry and the given values. If this topic is new to you, clike Reveal answers for the first time and click Advice.

Before starting, check that your calculator is in degrees mode by verifying that $\\cos{60} = \\frac{1}{2}$.

(If your calculator does not give this answer, press SHIFT $\\rightarrow$ SETUP $\\rightarrow$ 3 to enter degrees mode if using a Casio $fx$ model calculator, otherwise refer to your calculator's manual.)

", "advice": "

Each angle on a triangle is connected to two sides and is facing another.

The longest side of the triangle is always the hypotenuse.

The other side that makes the angle is called the adjacent.

The final side not connected in any way to the angle is called the opposite.

(Note that we only call the longest side the hypotenuse if we have a right-angled triangle. We cannot apply SOHCAHTOA or Pythagoras' Theorem to triangles which are not right-angled, so we would use the sine or cosine rules instead.)

For example, using the image below, you can see which side is denoted by each term from the highlighted angle's perspective.

One of the ways you can approach this style of question is by using SOHCAHTOA.

This can be written more visually as

\\[\\text{S}^\\text{O}_\\text{H}\\space\\text{C}^\\text{A}_\\text{H}\\space\\text{T}^\\text{O}_\\text{A}\\]

It represents each trigonometric function and what they are equivalent to.

Written out in full, we would have:

SIN: opposite / hypotenuse

COS: adjacent / hypotenuse

TAN: opposite / adjacent

For example, $\\sin$ is represented by the first S.

If we were given an angle, say of $30^\\circ$,

$\\sin(30^\\circ)=\\frac{\\text{opposite}}{\\text{hypotenuse}}$

Evaluating $\\sin(30^\\circ)=\\frac{1}{2}$, we now know that $\\frac{\\text{opposite}}{\\text{hypotenuse}}=\\frac{1}{2}$

If we were given one of these sides, we would then be able to work out the other one by multiplying accordingly.

Similarly if we were given two sides, and told to work out a specific angle, we could.

Referring to the image above, suppose we want to find the highlighted angle and we are given that the hypotenuse is equal to $5$ units, and the adjacent is $4$ units.

We would determine from SOHCAHTOA that we need to use cos since we have the values for A and H.

So, $\\cos(x)=\\frac{4}{5}$

Hence, $x=\\cos^{-1}(\\frac{4}{5})=36.87^\\circ$

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Find sin/cos/tan of angle x in triangle (use \"sqrt\" for square root)

$a=\\var{a[6]}$

$b=\\var{b[6]}$

$\\sin(x) =$ [[0]], $\\cos(x) =$[[1]], $\\tan(x) =$ [[2]]

use the definitaions of $\\sin, \\cos$ and $\\tan$

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$x=\\var{x[4]}^\\circ$

$y=$ [[0]]$^\\circ$

For this question, use the principle that the interior angles in any triangle always add up to $180^\\circ$

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$c=\\var{a[0]}$

$x=\\var{x[0]}^\\circ$

$a=$ [[0]] (Give your answer to two decimal places)

Use CAH to answer this question as you know the values of the side adjacent to the angle and the hypotenuse.

Cos(x)=a/c

You have not given your answer to the correct precision.

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$c=\\var{fh}$

$a=\\var{fa}$

$x=$ [[0]]$^\\circ$ (Give your answer to two decimal places)

You have not given your answer to the correct precision.

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$x$ is given and (sin(x),cos(x)) is plotted on a unit circle. Then the student is asked to determine sin(y) and cos(y), where y is closely related to x (e.g. y=-x, y=180+x, etc.) Also find values and sign of cos/tan/sin(x).

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The slope of the line.

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The y-intercept.

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{dragpointa(x[0],y[0])}

Use the diagram above to determine $\\sin(\\var{angle[0]}^{\\circ})$ and $\\cos(\\var{angle[0]}^{\\circ})$. To get to point $A$, we started at $(1,0)$ and rotated by $\\var{angle[0]}^{\\circ}$. If you hover the mouse over the point $A$, you will be shown its coordinates.

Give your answer to 2 d.p..

$\\sin(\\var{angle[0]}^{\\circ}) =$ [[0]]

$\\cos(\\var{angle[0]}^{\\circ}) =$ [[1]]

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Find the point $(x,y)$ on the unit circle when A= {teta[index]}$^\\circ$

(Give your answers to two decimal places):

$x$ = [[0]]

$y$ = [[1]]

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The time has run out.

"}, "timedwarning": {"action": "warn", "message": "

5 minutes until time will run out.

"}}, "feedback": {"enterreviewmodeimmediately": true, "showactualmarkwhen": "inreview", "showtotalmarkwhen": "inreview", "showanswerstatewhen": "inreview", "showpartfeedbackmessageswhen": "inreview", "showexpectedanswerswhen": "inreview", "showadvicewhen": "inreview", "allowrevealanswer": false, "intro": "

Instructions:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n

1.	Complete the questions within 90 minutes and achieve 80% or higher.
2.	You can take this self-assessment as many times as you need, until you receive a satisfactory grade (you don't need to achieve 80% when you 'give it a go' the first time)
3.	Use the \"Print this results summary\" and save as a pdf after you complete your attempt. You will need the printout showing all questions for your module submission.

", "end_message": "", "results_options": {"printquestions": true, "printadvice": true}, "feedbackmessages": [{"message": "

Congratulations! You have achieved the minimum threshold for this module's self-assessment.

Use the \"Print this results summary\" and save your attempt as a pdf. You will need the printout showing all questions for your module submission.

", "threshold": "80"}, {"message": "

Unfortunately you have not achieved the minimum score.

If this is your first 'Give it a go' attempt - don't despair! This is exactly why we take our first attempt - to see how we're going and whether we need more practice in order to complete the quest.

You should still use the \"Print this results summary\" option to save a copy of your results as a pdf, which will help with your learning and can also be shared with your tutors so they can help with certain questions.

If you have tried this test several times and have not been able to pass, then it is strongly advised that you attend class to go over your results with the teaching team. You can attempt the quiz while in class, and discuss your results with the tutors. Do not attempt to try to solve this quiz on your own without understanding your mistakes first. You will likely end up spending far more time than necessary on the module.

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