i realy need help with these!!
1.cot 30° (give answer in simplest radical form
2.csc 30° (give answer in simplest radical form.
3.sin 60° (give answer in simplest radical form.
4.tan 60° (give answer in simplest radical form.
5.sec 60° (give answer in simplest radical form.
6.cos 45° (give answer in simplest radical form.
7.sec 45° (give answer in simplest radical form.
8.cot 60° (give answer in simplest radical form.
i would really appreciate some help.....please!!
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Answers & Comments
Where do you need help?
Each of these is a simply defined ratio taken from one of your "special" triangles.
The fact that you can't get even the simplest (#3, #6) shows that you haven't bothered to consult your textbook, your class notes, or a trivial web search; you haven't drawn and labeled the triangles. These are required by the guidelines before you post here.
That said, I expect that you're going to need the table I gave my trig students.
It contains the only angles you have to memorize for the quizzes & tests.
It's not in the simplest form, but it's easy to remember, and reducing the roots is simple
sin 00 = cos 90 = √0 / 2 = 0
sin 30 = cos 60 = √1 / 2 = 1/2
sin 45 = cos 45 = √2 / 2
sin 60 = cos 30 = √3 / 2
sin 90 = cos 00 = √4 / 2 = 1
See how easy? That column with the radicals is the critical one.
Now, for the other trig functions:
tan = sin / cos
cot = 1/tan
sec = 1/cos
csc = 1/sin
That and trivial algebra are all you need to know.
Can you do these now? If not, you'll have to explain where you need help.
Right triangles with a 30º angle or 30º, 60º, 90º , have opposite sides in
proportion to: 1 : √3 : 2
tan[30º] = 1 ⁄ √3 cot[30º] = √3
sin[30º] = 1 ⁄ 2 csc[30º] = 2
cos[30º] = (√3) ⁄ 2 sec[30º] = 2 ⁄ √3
tan[60º] = √3 cot[60º] = 1 ⁄ √3
sin[60º] = (√3) ⁄ 2 csc60º] = 2 ⁄ √3
cos[60º] = 1 ⁄ 2 sec[60º] = 2
Right triangles with a 30º angle or 45º, 45º, 90º , have opposite sides in
proportion to: 1 : 1 : √2
tan[45º] = 1 cot[45º] = 1
sin[45º] = 1 ⁄ √2 csc[45º] = √2
cos[45º] = 1 ⁄ √2 sec[45º] = √2
1. Rectangular root of 48 + square root of three = ( 16 x three )^zero.5 + ( 3 ) ^zero.5 = 4 ( 3) zero.5 + 1 (three)^0.5 = 5 ( 3)^zero.5 or 5 x square root of three question 2 is not clear. 3. -four*sqaure root of ab *three rectangular root of b = -12 b square root of a.