# Thread: Two quick Trig question I am stuck on.

1. ## Two quick Trig question I am stuck on.

(Problem 1.)
---

The equation for the angle formed by a rhythmically moving object, y, is given below, where t is time (in seconds):

y = (1/6)(sin( ((5)(pi)(t)) / (4) )

# or "(1/6)(sin( (5 times pi times t) divided by (4))

(a) Solve the equation for t.
(b) At what time(s) does the object form an angle of 0.1 radian?

----

So, the first part of the problem that I do not understand is how to solve for t when there are 2 variables. Without knowing how to solve for t, I do not know how to complete the second part of the problem.

--------------

(Problem 2.)
---

Solve each triangle ABC that exists. Angles in DMS (Degrees Minutes Seconds).
C = 29(DEG)50(MINUTES), a = 8.61, c = 5.21

----

Just some additional info to clear up some possible confusion: The lower case letters 'a' and 'c' represent triangle sides, while upper case 'C' represents the angle C across from side 'c'.

I can get as far as finding that there are 2 triangles (ambiguous case), but I am stuck at that point.
--------------

Your help would be VERY greatly appreciated, thank you all in advance.

2. ## Re: Two quick Trig question I am stuck on.

Problem 1

a) $6y=\sin \left(\frac{5\pi \cdot t}{4}\right) \Rightarrow \frac {5\pi \cdot t}{4}=\arcsin (6y) \Rightarrow t=\frac{4\arcsin(6y)}{5\cdot \pi}$

b) $\frac{5 \pi \cdot t}{4}=0.1 \Rightarrow t=\frac{4 \cdot 0.1}{5\cdot 3.14}$

Problem 2

$\frac{a}{\sin A}=\frac{c}{\sin C}$

$A+B+C=180$

$b^2=a^2+c^2-2ac\cos B$

3. ## Re: Two quick Trig question I am stuck on.

I appreciate your help, but I have a question. What happened to the 6 in 1.B?

4. ## Re: Two quick Trig question I am stuck on.

Originally Posted by trigGirl1990
I appreciate your help, but I have a question. What happened to the 6 in 1.B?
Angle is represented by expression : $\frac{5 \pi \cdot t}{4}$

so it doesn't matter if there is $6$ or $666$

5. ## Re: Two quick Trig question I am stuck on.

Correct me if I'm wrong, but I believe the angle is represented by 'y' in y = (1/6)(sin( ((5)(pi)(t)) / (4) ) .

6. ## Re: Two quick Trig question I am stuck on.

Originally Posted by trigGirl1990
Correct me if I'm wrong, but I believe the angle is represented by 'y' in y = (1/6)(sin( ((5)(pi)(t)) / (4) ) .
We can say that $\arcsin(6\cdot y)= 0.1$ rad

Do you understand now ?

7. ## Re: Two quick Trig question I am stuck on.

I don't see how you are getting that. The problem states "The equation for the angle formed by a rhythmically moving object, y, is given below"

Let y = 0.1 rad
# y never changes, it is never reassigned.
arcsin((6)(.1)) != 0.1 rad

It looks like you're trying to say that arcsin((6)(y)) = y

if y = 0.1, how can y = arcsin((6)(y)) ?

8. ## Re: Two quick Trig question I am stuck on.

Originally Posted by trigGirl1990
I don't see how you are getting that. The problem states "The equation for the angle formed by a rhythmically moving object, y, is given below"

Let y = 0.1 rad
# y never changes, it is never reassigned.
arcsin((6)(.1)) != 0.1 rad

It looks like you're trying to say that arcsin((6)(y)) = y

if y = 0.1, how can y = arcsin((6)(y)) ?
You are correct I misread the question :

1b) $t=\frac{4\arcsin(6\cdot 0.1)}{5 \cdot 3.14}$