#1**+10 **

tan theta = sin theta / cos theta

sin theta / cos theta = 1

sin theta = cos theta

If sin theta < 0, **then cos theta must be equal to sin theta in order for tan theta to equal 1.**

2 cos x = -1

cos x = -1/2

We would be looking at the 2nd quadrant...x has to be **120 degrees or 2pi/3.**

AzizHusain Aug 23, 2014

#1**+10 **

Best Answer

tan theta = sin theta / cos theta

sin theta / cos theta = 1

sin theta = cos theta

If sin theta < 0, **then cos theta must be equal to sin theta in order for tan theta to equal 1.**

2 cos x = -1

cos x = -1/2

We would be looking at the 2nd quadrant...x has to be **120 degrees or 2pi/3.**

AzizHusain Aug 23, 2014

#2**0 **

for Q 5 ... so waht is the answer of the question !!!

for Q 6 ... the answer in the model answer is +and - ** 2pi/3**

xvxvxv Aug 24, 2014

#3**+5 **

5. The sin is < 0 in quadrants 3 and 4. And the cos < 0 in quadrants 2 and 3. But the sin and the cos would have to have the same sign for the tangent to be positive. Thus, theta is a 3rd quadrant angle. And since the tan(theta)= 1 at 45 degrees, this is a 45 degree angle in quadrant 3. And the cos of 45 degrees = 1/√2, or √2/2, if you prefer. But, since the cos is negative in this quadrant, then cos(theta) = - 1/√2 = -√2/2.

6.

2 cos x = -1 divide both sides by 2

cos x = -1/2 .... this occurs at (2/3)pi in the interval [0, pi) and at -(2/3)pi in the interval [-pi, 0]. The second answer may be a little hard to see. Note that cos x = -1/2 at (4/3)pi. But, subtracting 2*pi from this gives us -(2/3)pi.......

CPhill Aug 24, 2014