# Thread: Choose the point on the terminal side of theta.

1. ## Choose the point on the terminal side of theta.

Hello! I ran onto these twos problem on one of my assignments. We're only a few weeks into this semester and I'm not sure how to solve these without a calculator.. Could someone please help me start to solve it or solve them for me(step-by-step)? Thank you so much!

"Without using a calculator, choose the point on the terminal side of theta.
1). theta = 5pi/4"

and

"Evaluate without using a calculator.
2). sin theta, if cos theta=2/5 and tan theta<0"

Thank you very much!

2. ## Re: Choose the point on the terminal side of theta.

If you have a point,$(x,y)$ that is $r$ units out along a line that is $\theta$ radians from the x-axis then

$(x,y) = (r \cos(\theta, r \sin(\theta))$

For problem (1)

$r=1,~\theta = \dfrac {5\pi}{4}$

$(x,y) = \left(1\cdot \cos\left(\dfrac {5\pi}{4}\right),1\cdot \sin\left(\dfrac {5\pi}{4}\right) \right)$

Can you evaluate that without a calculator? Use the Pythagorean theorem if you need to.

For problem (2)

note that $\sin^2(\theta) + \cos^2(\theta)=1$

and select from the two possible values of $\sin(\theta)$ using the information on the tangent

3. ## Re: Choose the point on the terminal side of theta.

Originally Posted by Venusian
Hello! I ran onto these twos problem on one of my assignments. We're only a few weeks into this semester and I'm not sure how to solve these without a calculator.. Could someone please help me start to solve it or solve them for me(step-by-step)? Thank you so much!
"Without using a calculator, choose the point on the terminal side of theta.
1). theta = 5pi/4"
Had I written this question, I would have expected you to know that $\dfrac{5\pi}{4}$ is in III and and has reference angle of $\dfrac{\pi}{4}$.
Therefore any point on its terminal ray has ordinates $\bf{t}\left(\dfrac{\sqrt2}{2},\dfrac{\sqrt2}{2} \right),~\bf{t}<0$

That is as random as it gets.