# If sin of theta equals 3/8 and theta is in quadrant II. what are cos, tan, csc, cot, and sec of theta?

##### 2 Answers

See explanation below.

#### Explanation:

Imagine a right triangle being drawn on the cartesian plane, as in the following example.

Since sin = opposite/hypotenuse, the side opposite to

So, now we know that the adjacent side measures

Now, for

Therefore,

To summarize, the six trigonometric ratios, we get:

Hopefully this helps!

#### Explanation:

#sintheta=3/8to(color(red)(1))#

#• csctheta=1/sintheta=8/3to(color(red)(2))#

#• costheta=+-sqrt(1-sin^2theta)#

#color(white)(xxxxx)=-sqrt(1-9/64)larr" negative value"#

#color(white)(xxxxx)=-sqrt(55/64)#

#rArrcostheta=-sqrt55/8to(color(red)(3))#

#• sectheta=1/costheta=-8/sqrt55to(color(red)(4))#

#• tantheta=(sintheta)/(costheta)#

#color(white)(xxxx)=3/8xx-8/sqrt55=-3/sqrt55to(color(red)(5))#

#• cottheta=1/tantheta=-sqrt55/3to(color(red)(6))#