Exact Value of sin(-315°)

[ErionK]

What is the exact value of sin(-315°)? I can't get any of these answers
a) -(2)^1/2
b) (2)^1/2
c) -1/(2^1/2)
d) 1/(2^1/2)

 

[Steven G]

So what answer did you get?
Did you draw a triangle? Can we see it?
It is hard to offer help when no work is shown.

 

[The Highlander]

What is the exact value of sin(-315°)? I can't get any of these answers
a) -(2)^1/2
b) (2)^1/2
c) -1/(2^1/2)
d) 1/(2^1/2)

Hi ErionK,

Do you know all your “Exact Values”?

Start by copying and completing the worksheet below into your workbook(s).

You should copy this (completed) worksheet into the front or back of all your Maths workbooks unless and until you are confident that you know all these results by heart.

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Now that you do know all the “Exact Values” for the most frequently encountered trigonometric ratios, the diagram below may help you decide which of the answers is correct:-

\(\displaystyle a. -\sqrt{2}\)

\(\displaystyle b.   \sqrt{2}\)

\(\displaystyle c. -\frac{1}{\sqrt{2}}\)

\(\displaystyle d.   \frac{1}{\sqrt{2}}\)

From the diagram, what is -315° the same as?

(Hint: Consider the amount of turn indicated by the Red Arrow.)

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[lookagain]

a) -(2)^1/2
b) (2)^1/2
c) -1/(2^1/2)
d) 1/(2^1/2)

You must write the fractional exponents inside of grouping symbols:

a) -2^(1/2)
b) 2^(1/2)
c) -1/2^(1/2)
d) 1/2^(1/2)

 

[pka]

[imath]-\dfrac{7\pi}{4} \equiv \dfrac{\pi}{4}[/imath] thus what [imath]\sin\left(\dfrac{\pi}{4}\right)=~?[/imath]
[imath][/imath][imath][/imath][imath][/imath]

 

[The Highlander]

[imath]-\dfrac{7\pi}{4} \equiv \dfrac{\pi}{4}[/imath] thus what [imath]\sin\left(\dfrac{\pi}{4}\right)=~?[/imath]
[imath][/imath][imath][/imath][imath][/imath]

That is very true, pka, but, given that the OP is struggling already with the question, converting from degree to radian measure may confuse her/him even further and how is s/he supposed to understand the (perfectly correct) equivalence that you state? (ie: [imath]-\dfrac{7\pi}{4} \equiv \dfrac{\pi}{4}[/imath])

 

[Shivam18]

The answer is [imath]1/\sqrt2[/imath]. [imath]-315 \degree[/imath] is same as [imath]45 \degree[/imath] from the x axis. So you can calculate [imath]sin(45\degree)[/imath] to get your result which is [imath]1/\sqrt2[/imath].