Homework Help: math

Posted by hannah on Tuesday, February 8, 2011 at 12:42pm.

if csc theta= -5/3 and theta has its terminal side in quadrant III, find the exact value of tan 2 theta.

math - MathMate, Tuesday, February 8, 2011 at 5:16pm
csc(θ)=-5/3
1/sin(θ)=-5/3
sin(θ)=1/(-5/3)=-3/5
cos(θ)=-√(1-(-3/5)²)
=-4/5
tan(θ)=sin(θ)/cos(θ)
=(-3/5)/(-4/5)
=3/4
tan(2θ)=2tan(&theta))/(1-tan²(θ))
=2(3/4)/(1-(3/4)²)
=3.43
(note: 2θ is in the first quadrant.

Related Questions

Math - 1. Let (-7, 4) be a point on the terminal side of (theta). Find the exact...
Pre-Calculus-check answers - If cos theta = 0.8 and 270<theta<360...
trig - If sin theta is equal to 5/13 and theta is an angle in quadrant II find ...
trig - Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the ...
trig - Let (theta) be an angle in quadrant II such that csc(theta)=8/5 Find the ...
Trigonometric Functions - Determine the Value of all six trigonometric functions...
Trig - 1. Establish the identity: sin(theta+3pi/2)=-cos(theta) 2. Find the exact...
Math - Let (3,-2) be a point on the terminal side of theta. Find cos theta, csc ...
easy trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...
simple trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...

For Further Reading

First Name:
School Subject:
Answer: