Thread: solving trigonometry questions

1.
prove that cosAcos(30-A)cos(30+A)= 1/4 cos3A
Hence, evaluate cosAcos(30-A)cos(30+A) when A= 170 degree;
give your answer in exact value.

2.
Assuming r is positive, find r and the value of θ between -180degree and 180 degree which satisfy the questions:
r cos θ= -6 and r sin θ= 1.5
Give your answer to the nearest minute.

Originally Posted by kelvinchy

1.
prove that cosAcos(30-A)cos(30+A)= 1/4 cos3A
Hence, evaluate cosAcos(30-A)cos(30+A) when A= 170 degree;
give your answer in exact value.

2.
Assuming r is positive, find r and the value of θ between -180degree and 180 degree which satisfy the questions:
r cos θ= -6 and r sin θ= 1.5
Give your answer to the nearest minute.

for#1, you'll need to use the cosine sum/difference identity for both the cosine sum and difference factors on the left side ... then simplify. then you'll need to rewrite the right side as and use the same identity to expand and simplify this expression. bottom line is ... lots of grunt work algebra in front of you.


for #2, note the polar/cartesian equations below ...







since is in quad II ,