fundamental identities

[Princezz3286]

this is one of my homework problems that i need help with the others are the same style but i need a better example than the one they give in my book. The problem asks us to find sin theta. Given information: sec of theta= 11/4, tan theta is less than 0.

1) I determined that this angle is located in quadrant one because sec is equal to 1/cos. cos = x where x in this case is positive.

2) I used the pythagorean iD tan^2 theta + 1 = sec^2 theta and got tan^2 theta equal to square root of 117/4, then took the square root of that to find tan.

because we know tan = sin/cos.

now i know tan and cos, but where do i go from here? or did i already blow it? Please help!

Thanks!

 

[Loren]

this is one of my homework problems that i need help with the others are the same style but i need a better example than the one they give in my book. The problem asks us to find sin theta. Given information: sec of theta= 11/4, tan theta is less than 0.

1) I determined that this angle is located in quadrant one because sec is equal to 1/cos. cos = x where x in this case is positive. <<< Although cosine is positive in QI, it is also positive in QIV. It says tan theta is negative. Tan theta is not negative in QI.

2) I used the pythagorean iD tan^2 theta + 1 = sec^2 theta and got tan^2 theta equal to square root of 117/4, then took the square root of that to find tan. <<< Once you figure out which quadrant theta is in, you might draw a sketch of the angle, since you know that cosine theta = 4/11. Draw your sketch so that the leg of the triangle on the x axis is about 4 units long and the hypotenuse is about 11 units long. Then use the Pythagorean Thm to determine the length of the long leg. Then determine the sin of theta by looking at your sketch

because we know tan = sin/cos.

now i know tan and cos, but where do i go from here? or did i already blow it? Please help!

Thanks!

 

[Princezz3286]

thanks for the help!