Hi my name is Patty and I am taking a pre-calculus course and need help with the following.
Question
If sin0 = 7/8 and 0 is in quadrant 2, find the other
five trigonometric
functions of 0. (report your answers in radical form)
I'm also not sure
how to show (0) with a line through it so I have just used
the zero key.
What is radical form?
would this be how I answer this?
sin2 0 + cos2 0 = 1
(7/8)2 + cos2 0 = 1
cos2 0 = 1 - 49/64 = 15/64
cos 0 = sq root of 15/64 = 1/8 sq root 15
and
tan 0 = sin 0/cos 0 = 7/8 / 1/8 sq root 15
= 7/sq root 15 (not sure about the math here?)
= 1.8
and
cot 0 = 1/tan0 = 1/ 7/sq root 15 = sq root 15/ 7
= .55
and
sec 0 = 1/cos 0 = 1/ 1/8 sq root 15
= 1/8 sq root 15
= .48
and
csc 0 = 1/sin 0 = 1/ 7/8 = 8/7 = 1 1/7
does any of this make sense and if so is it right?
Thank you
Patty
Hi Patty,
You missed one important point in the question, the fact that the angle is in the second quadrant. (I am going to use t for theta, rather than O. I worry about confusing O with 0.)
I agree with your solution to the fact that
cos2 t = 1 - 49/64 = 15/64
but, since t is in the second quadrant, cos t is negative. Thus
cos t = - 1/8
sq root 15
This is cos t in radical form, It involves rational numbers and roots, but no decimals.
Since the tangent is the sine over the cosine
tan t = - 7/sq root 15
(don't use the decimal approximation, leave the answer in this form.)
For the remainder of the problem make sure that you check the signs and remove the decimal approximations.
Penny