Question

Given the cos =3/5 and son of theta is less than 0 state A) the quadrant of the angle and B) other five trig function values

Answer 1

Given:

`\begin{gathered} cos\text{ }\theta=(3)/(5) \\ sin\text{ }\theta<0 \end{gathered}`

We will find the following:

A) the quadrant of the angle.

the cosine of the angle is positive in two quadrants the first and the fourth

In the first quadrant, the sine is (+v)

while in the fourth quadrant the sine is (-v)

So, for the given angle, the angle lying in Q4

B) other five trig function values.

The hypotenuse = h = 5

the adjacent = x = 3

The opposite = y = ±√(5^2 - 3^2)= ±√16 = -4

Choose the (-ve) value because the angle lying in Q4

So, the trig functions will be as follows:

`\begin{gathered} sin\text{ }\theta=(opposite)/(hypotenuse)=-(4)/(5) \\ \\ tan\text{ }\theta=(opposite)/(adjacent)=(-4)/(3) \\ \\ sec\text{ }\theta=\frac{1}{cos\text{ }\theta}=(5)/(3) \\ \\ cosec\text{ }\theta=\frac{1}{sin\text{ }\theta}=(5)/(-4) \\ \\ cot\text{ }\theta=\frac{1}{tan\text{ }\theta}=(3)/(-4) \end{gathered}`