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given sin t = 1/7, tan t<0, find cos(t) and tan(t)

 Apr 15, 2015

Best Answer 

 #1
avatar+529 
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Draw yourself a right-angled triangle, one side horizontal and the other vertical. Now, make the vertical side of length 1 and the hypotenuse of length 7, because this defines our angle whose sine is 1 divided by 7. Let's mark that angle as angle t. Make sure you are labelling the correct angle! It's the one where sine t = 1 divided by 7, and there's only one that can be correct here.

 

Use Pythagoras' Theorem to determine the length of the only unknown side, that's the horizontal side. I'll leave it to you to do that for yourself.

 

Now that you know all sides, you can look at our angle t and write down its cosine as the ratio of the lengths of two sides. (Remember the rule, cos = adjacent/hypotenuse)

 

Then write down tangent of t as the ratio of two sides.

 

You've got it!

That was fun!! 

 Apr 15, 2015
 #1
avatar+529 
+5
Best Answer

Draw yourself a right-angled triangle, one side horizontal and the other vertical. Now, make the vertical side of length 1 and the hypotenuse of length 7, because this defines our angle whose sine is 1 divided by 7. Let's mark that angle as angle t. Make sure you are labelling the correct angle! It's the one where sine t = 1 divided by 7, and there's only one that can be correct here.

 

Use Pythagoras' Theorem to determine the length of the only unknown side, that's the horizontal side. I'll leave it to you to do that for yourself.

 

Now that you know all sides, you can look at our angle t and write down its cosine as the ratio of the lengths of two sides. (Remember the rule, cos = adjacent/hypotenuse)

 

Then write down tangent of t as the ratio of two sides.

 

You've got it!

That was fun!! 

Badinage Apr 15, 2015

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