Question

Find cot θ if csc θ = negative square root of thirty seven divided by six divided by six and tan θ > 0.

Answer 1

@IMStuck

Answer 2

@IMStuck

Answer 3

I'm here! Let me take a look!

Answer 4

\[\csc \theta=\frac{ \frac{ -\sqrt{37} }{ 6 } }{ 6 }\]?

Answer 5

No, its \[\csc \theta=-\frac{ \sqrt{37} }{ 6 }\]

Answer 6

Oh that is so much better! NOW let me look... ; )

Answer 7

The first thing I did was to convert the csc to sin. Do you know the relationship between csc and sin?

Answer 8

csc=1/sin

Answer 9

That's right, so to find the sin of the given angle, just flip the fraction. If \[\csc \theta=-\frac{ \sqrt{37} }{ 6 }\]then \[\sin \theta=-\frac{ 6 }{ \sqrt{37} }\]Now that that's out of the way...

Answer 10

The second thing we need to deal with is the fact that they told you that the tangent is > 0, meaning it is positive. Do you know what tangent is in terms of sin and cos?

Answer 11

tan=sin/cos

Answer 12

Cool. Now where is tangent positive? Which 2 quadrants? There are 2.

Answer 13

1 and 3

Answer 14

Good good....BUT

Answer 15

they tell you that the sin of the angle is -6/sqrt 37. So it has to be in the quadrant in which sin (the y value) is negative. In which quadrant is the sin negative...I or III?

Answer 16

3

Answer 17

Still with me? We're about done! Keep up the good hard work! This isn't easy stuff at all!!!

Answer 18

You're right QIII. So here's a pic so far:

Answer 19

We need to find x. How do we do that?

Answer 20

sqrt(37)^2--6^2=b^2

Answer 21

good.....

Answer 22

37-36=b^2
1=b^2
1=b

Answer 23

Ok...NEXT is to convert cotangent into sin and cos. What is that identity?

Answer 24

cot theta = ???

Answer 25

cot=cos/sin

Answer 26

Wow! You really know your stuff! Good job! Ok, if cot= cos/sin, we need to find that using the values of the triangle we drew.

Answer 27

what are cos and sin?