math
posted by mathstudent .
Prove that for all real values of a, b, t (theta):
(a * cos t + b * sin t)^2 <= a^2 + b^2
I will be happy to critique your work. Start on the left, square it,
(a * cos t + b * sin t)^2 =
a^2 (1  sin^2t) + 2ab sin t cost+ b^2 (1  cos^2 t)=
a^2 + b^2  (a sin t  b cos t)^2
<= (a^2 + b^2)
because (a sin t  b cos t)^2 mus be positive or zero.
I don't know how you figured that out, but thanks. That works perfectly!
Respond to this Question
Similar Questions

algebra
Can someone please help me do this problem? 
calculus
conic sections prove that the line x2y+10=0 touches the ellipse 9x^2+64y^2=576 show that the equation of the normal to the ellipse x^2/a^2 + y^2/b^2 = 1 at the point (a cos theta, b sin theta ) is ax sin theta  by cos theta  (a^2b^2) … 
Mathematics  Trigonometric Identities
Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y … 
math
There are no typos and no work b/c I don't know how to do them. Thanks. 1)Find cos theta if sin theta=3/5 and 90 degrees<theta<180 degrees. A)4/5 B)4/5 C)square root of 34/5 D)square root of 34/5 I chose A 2)Simplify:1csc^2theta/cot^2theta … 
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 … 
Math Trig
1. Determine the exact value of cos^1 (pi/2). Give number and explanaton. 2. Determine the exact value of tan^1(sq. root 3). with explanation. 3. Determine exact value of cos(cos^1(19 pi)). with explanation. 4. Determine the exact … 
Precalculus with Trigonometry
Prove or disprove the following Identities: cos(x)  sin(x) = cos(x) + sin (x) sin raised to the 4 (theta)  cos raised to the 4 (theta) = sin squared (theta)  cos squared (theta) cos (x+(pi)/(6)) + sin (x  (pi)/(3)) = 0 cos(x+y)cos(xy) … 
math
I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = 2/3, which of the following are possible? 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank … 
Trigonometry
Prove the following identities: 1. (tan theta  sin theta)^2 + (1cos theta)^2 = (1sec theta) ^2 2. (12cos^2 theta) / sin theta cos theta = tan theta  cot theta 3. (sin theta + cos theta ) ^2 + (sin theta  cos theta ) ^2 = 2 Thank …