PreCalculuscheck answers
posted by Lucy .
If cos theta = 0.8 and 270<theta<360, find the exact value of sin 2theta
a) 0.96
b) 0.6
c) 0.96
d) 0.28
Answer: b
2) If csc theta = 5/3, and theta has its terminal side in Quadrant III, find the exact value of tan 2theta
a)24/25
b) 7/25
c) 24/7
d) 7/25
Thanks

1) cosθ=0.8 , θ is in fourth quadrant
θ= cos^(1)0.8=36.86989765 + 270=306.87
so , sin 2θ= sin2(306.87)= 0.96
answer : a 
2) csc Ø = 5/3, then sin Ø = 3/5 and is in III
the cos Ø = 4/5
so tan 2Ø = sin 2Ø/cos 2Ø
= 2sinØcosØ/(cos^2 Ø  sin^2 Ø)
=2(3/5)(4/5)/(16/25  9/25)
= 24/7 
1) cscθ = (5/3) , θ is in third quadrant
1/sinθ = (5/3) => sinθ= 3/5
θ= 36.8699
θ is in third quadrant
so θ = 36.8669+180 = 216.8669
tan2θ = tan2(216.8669) = 3.42724 = 24/7
answer : c 
When a trig question asks for "exact" value, a calculator is not to be used, and all work has to be shown with exact values.
24/7 is not equal to 3.42724 
thanks for note Reiny .
Respond to this Question
Similar Questions

Algebra II
Which of the following expressions are not equal to 1? 
Calculus
I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure … 
Pre Calc.
Use the sum or difference identity to find the exact value of sin255 degrees. My answer: (sqrt(2) sqrt(6)) / (4) Find the value of tan (alphabeta), if cos alpha= 3/5, sin beta= 5/13, 90<alpha<180, and 90<beta<180. My … 
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) and … 
Algebra II
Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)Which expression is equivalent to tan(theta)(sec(theta))/(sin(theta))? 
Trig
1. Establish the identity: sin(theta+3pi/2)=cos(theta) 2. Find the exact value of 2(theta) if sin(theta)=5/13 3. Show that: csc2(theta)cot2(theta)=tan(theta) 4. Find the exact value of tan(cos^1(square root of 3/2) 5. Approximate … 
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.) Simplify … 
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.) Simplify … 
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. 
Precalculus
Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment …