PQRS Parallelogram Help: Find Sin Q with Working

In summary, In a parallelogram, opposite angles are congruent and adjacent angles are supplementary. Therefore, if sin P = k, then sin Q = -k.
  • #1
Solidmozza
29
1
Hi, New to this forum.
Im just doing my school certificate (yr10) and need help with 1 question.

PQRS is any parallelogram. If sin P = k, find Sin Q

Probably sounds like a stupid question but heck if you can give me the answer with working id be really happy. :biggrin: thanks
 
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  • #2
In a parallelogram opposite angles are congruent (angles P and R) and adjacent angles are supplementary (angle P and Q). sin Q= sin (pi- P).
 
  • #3
Solidmozza said:
Hi, New to this forum.
Im just doing my school certificate (yr10) and need help with 1 question.

PQRS is any parallelogram. If sin P = k, find Sin Q

Probably sounds like a stupid question but heck if you can give me the answer with working id be really happy. :biggrin: thanks

2q + 2p = 360
q + p = 180
q = p-180
k=sin(p)
P=arcsin(k)
q=p-180
q=arcsin(k)-180
sin(q) = sin(arcsin(k)-180)
sin(q) = -sin(arcsin(k))
sin(q) = -k
 

FAQ: PQRS Parallelogram Help: Find Sin Q with Working

What is a PQRS parallelogram?

A PQRS parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides are equal in length and the opposite angles are also equal. It is also known as a rhombus or a diamond shape.

How do I find the value of sin Q in a PQRS parallelogram?

To find the value of sin Q in a PQRS parallelogram, you will need to know the length of one side and the measure of one angle. Once you have this information, you can use the trigonometric function sin Q = opposite/hypotenuse to calculate the value of sin Q.

Can you provide a step-by-step working for finding sin Q in a PQRS parallelogram?

Sure, here are the steps to find the value of sin Q in a PQRS parallelogram:
1. Identify the length of one side and the measure of one angle in the parallelogram.
2. Draw a right triangle using one of the sides as the base and the opposite angle as the angle of interest (Q).
3. Label the sides of the triangle as opposite, adjacent, and hypotenuse.
4. Use the formula sin Q = opposite/hypotenuse to find the value of sin Q.
5. Convert the value to decimal or fraction form, if needed.

What are some common mistakes when finding sin Q in a PQRS parallelogram?

One common mistake is using the wrong length for the opposite and adjacent sides of the right triangle. Another mistake is not converting the angle measure to radians when using a calculator. It is also important to make sure the angle being used is actually the angle of interest (Q) and not a different angle in the parallelogram.

Are there any other methods for finding sin Q in a PQRS parallelogram?

Yes, you can also use the Law of Sines or the Law of Cosines to find the value of sin Q in a PQRS parallelogram. However, these methods may require more information about the parallelogram such as the length of another side or the measure of another angle.

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