# Thread: Few Trig Problems

1. ## Few Trig Problems

1. (cos^2)T/1-sinT to 1+sinT

Show the steps to get the left side to equal 1+sint

2. find an interval (0,2(pie)) to solve cotT= sqrt3/ 3

3. Determine the width of a river with markers placed at each side in line withe the base of a tower that rises 25m out of the ground. from the top of the tower, the angles of depression are 58 degrees and 38 degrees. how wide is the river?

2. 1)

First, check those parentheses. Please never write that again. Do not separate a function from its arguement.

Second, multiple numerator and denominator by "1+sin(T)"

2)

First, pie is for eating. pi is for mathematics.

Second, cot(T) = cos(T)/sin(T)

Let's see those two. Then we can talk about the third.

3. I apologize, I wasn't sure how to put the symbols on here. Im sure I confused you in my attempt to post those questions. I was also posting on my iphone, so typos happen frequently. You want me to rewrite the problems?

4. No, I was not confused. I already answered and provided methods to proceed. Just learn. There is no harsh judgment here.

5. I have no idea how to do the first two. Would you mind showing some steps? I tried putting something in to laTex to help make things clearer, but man that is another animal all on its own!
For the last word problem I have the answer to be 40 meters? tan=d/25 d=25*tan58 degrees??

6. Originally Posted by na300zx
I have no idea how to do the first two. Would you mind showing some steps? I tried putting something in to laTex to help make things clearer, but man that is another animal all on its own!
For the last word problem I have the answer to be 40 meters? tan=d/25 d=25*tan58 degrees??
1) I told you exactly how to do the first one in my first post. Did you try it?

2) Show us #1 and we can talk about #2.

3) "tan=d/25" Never write that again. "tan" means nothing by itself.

What is 'd'? Please define your terms.

I think you need two things.

x = Distance between tower and the near shore.
y = Width of the river.

Now it's thinking time.

Angle of depression to the far shore is 38º.
Angle of depression to the near shore is 58º, making the change for crossing the river 20º.
Angle of depression to the bottom of the tower is 90º, making the change for getting there from the river 32º.

Thus

$\displaystyle \tan(32^{\circ}) = \frac{x}{25}$

$\displaystyle \tan(52^{\circ}) = \frac{x+y}{25}$

Solve for y.

Let's see what you get.

7. For number 1 I wrote cos^2 as the Pythagorean identity and then used that as a difference of two squares. Which cancels 1-sin and leaves 1+sin.
Number 2 I got 4(pi)/3 and pi/3.

Number 3 idk yet

8. What will it look like when solved for y?

9. 1) Assuming that question asked is $\displaystyle Prove \frac{cos^2\theta}{1-sin\theta}=1+sin\theta$

$\displaystyle LHS= \frac{1^2-sin^2\theta}{1-sin\theta}$

$\displaystyle = \frac{(1-sin\theta)(1+sin\theta)}{1-sin\theta}$

$\displaystyle = (1)(1+sin\theta)$

$\displaystyle = 1+sin\theta$ (Proved)

10. Originally Posted by TKHunny
1)

First, check those parentheses. Please never write that again. Do not separate a function from its arguement.

Second, multiple numerator and denominator by "1+sin(T)"

2)

First, pie is for eating. pi is for mathematics.

Second, cot(T) = cos(T)/sin(T)

Let's see those two. Then we can talk about the third.

To prove a question, either prove from left to right or right to left...
Never multiply, divide, minus or add anything to both sides before starting to prove.