# calculus

let theta be an angle of quadrant IV such that sin theta = -8/9 find the exact value of sec theta and cot theta?

1. 👍
2. 👎
3. 👁
1. sin(Θ) = -8/9 = y/r

x = √(r^2 - y^2) = √17

sec(Θ) = r / x

cot(Θ) = x / y

1. 👍
2. 👎
2. third leg along x axis is sqrt (81-64) =sqrt (17)
so
x = sqrt (17)
y = -8
hypotenuse = 9
cos = sqrt (17) / 9
so sec = 1/cos = 9/sqrt 17
cot = sqrt (17) / -8

1. 👍
2. 👎
👤
Damon

## Similar Questions

1. ### Trigonometry

State the quadrant in which theta lies. sin(theta) > 0 and cos(theta) > 0 How can I determine this? Please explain.

2. ### Maths: Partial Differentiation

1) If x = rcos theta and y = r sin theta, show that partial r / partial x = cos theta and find partial theta / partial x. 2) If z = sin theta.sin phi.sin gamma, and z is calculated for the values theta = 30degrees, phi = 45

3. ### trig

write sec theta in terms of sin theta when theta lies in quadrant III

4. ### Math

1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact values of sin(theta), csc(theta), and cot(theta). 2. Let (theta) be an angle in quadrant IV such that sin(theta)=-2/5. Find the exact values of sec(theta)

1. ### Precalculus check answers help!

1.) Find an expression equivalent to sec theta sin theta cot theta csc theta. tan theta csc theta sec theta ~ sin theta 2.) Find an expression equivalent to cos theta/sin theta . tan theta cot theta ~ sec theta csc theta 3.)

2. ### trig

If sin theta is equal to 5/13 and theta is an angle in quadrant II find the value of cos theta, sec theta, tan theta, csc theta, cot theta.

3. ### trig

Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the exact value of tan(theta) and cos(theta).

4. ### math

Let theta be an angle in quadrant IV such that sin(theta)=-(2)/(5). Find the exact values of sec(theta) and tan(theta).

1. ### Calculus

Which one or ones of the following integrals produces the area that lies inside the circle r = 3 sin θ and outside the cardioid r = 1 + sin θ? (10 points) I. 1/2 the integral from pi/6 to 5pi/6 of 9*sin^2 theta minus (1 + sin