Given:
![\cos \theta =\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%5Cdfrac%7B3%7D%7B5%7D)
![\sin \theta](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3C0)
To find:
The quadrant of the terminal side of
and find the value of
.
Solution:
We know that,
In Quadrant I, all trigonometric ratios are positive.
In Quadrant II: Only sin and cosec are positive.
In Quadrant III: Only tan and cot are positive.
In Quadrant IV: Only cos and sec are positive.
It is given that,
![\cos \theta =\dfrac{3}{5}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%5Cdfrac%7B3%7D%7B5%7D)
![\sin \theta](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%20%3C0)
Here cos is positive and sine is negative. So,
must be lies in Quadrant IV.
We know that,
![\sin^2\theta +\cos^2\theta =1](https://tex.z-dn.net/?f=%5Csin%5E2%5Ctheta%20%2B%5Ccos%5E2%5Ctheta%20%3D1)
![\sin^2\theta=1-\cos^2\theta](https://tex.z-dn.net/?f=%5Csin%5E2%5Ctheta%3D1-%5Ccos%5E2%5Ctheta)
![\sin \theta=\pm \sqrt{1-\cos^2\theta}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D%5Cpm%20%5Csqrt%7B1-%5Ccos%5E2%5Ctheta%7D)
It is only negative because
lies in Quadrant IV. So,
![\sin \theta=-\sqrt{1-\cos^2\theta}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%5Ccos%5E2%5Ctheta%7D)
After substituting
, we get
![\sin \theta=-\sqrt{1-(\dfrac{3}{5})^2}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%28%5Cdfrac%7B3%7D%7B5%7D%29%5E2%7D)
![\sin \theta=-\sqrt{1-\dfrac{9}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B1-%5Cdfrac%7B9%7D%7B25%7D%7D)
![\sin \theta=-\sqrt{\dfrac{25-9}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B%5Cdfrac%7B25-9%7D%7B25%7D%7D)
![\sin \theta=-\sqrt{\dfrac{16}{25}}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Csqrt%7B%5Cdfrac%7B16%7D%7B25%7D%7D)
![\sin \theta=-\dfrac{4}{5}](https://tex.z-dn.net/?f=%5Csin%20%5Ctheta%3D-%5Cdfrac%7B4%7D%7B5%7D)
Therefore, the correct option is B.
The last one is 1 I believe
Answer:
220
Step-by-step explanation:
Now, I'm not sure if 220 is correct, but I'll explain my reasoning.
We know three angles of a triangle add up to 180 degrees.
So, the smaller triangle has 70 degrees and <em>a</em><em> </em>and <em>b</em><em> </em>variables. By virtue, <em>a</em><em> </em>+ <em>b</em><em> </em>+ 70 = 180.
So, <em>a</em><em> </em><em>+</em> <em>b</em><em> </em>= 110.
Likewise, when you look at the whole triangle, 70 degrees is also one of the angles while <em>c</em><em> </em>and <em>d</em><em> </em>are unknown.
So, <em>c</em><em> </em>+ <em>d</em> + 70 = 180.
This means <em>c</em><em> </em>+ <em>d</em><em> </em>= 110.
So, <em>(</em><em>a</em><em> </em>+<em> </em><em>b</em><em> </em>) +<em> </em><em>(</em><em>c</em><em> </em>+<em> </em><em>d</em><em> </em><em>)</em><em> </em><em>=</em><em> </em>
110 + 110 =
220 degrees.
I hope this helps!
Answer:
36 CDs
Step-by-step explanation:
32/2=16
16+20
36 CDs is your answer. Have a nice day!
Answer:
Step-by-step explanation:
Start at 1 1/3
Add the negative number.
1 1/3 + (-5/6)
Adding a negative number means to go left on a number line.
-5/6 is equal to -2/3 plus -1/6.
Move 2/3 to the left.
1 1/3 (Start)
1 (1/3)
2/3 (2/3)
Now, move 1/6th to the left.
2/3 is equal to 4/6
4/6 - 1/6 = 3/6
So, put the point at 3/6 or 1/2.